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Properties

Label 129...000.a
Order \( 2^{41} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47 \)
Exponent \( 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47 \)
Simple yes
$\card{G^{\mathrm{ab}}}$ \( 1 \)
$\card{Z(G)}$ 1
$\card{\Aut(G)}$ \( 2^{42} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47 \)
$\card{\mathrm{Out}(G)}$ \( 2 \)
Perm deg. $47$
Trans deg. not computed
Rank $2$

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Show commands: Gap / Magma / SageMath

Copy content magma:G := AlternatingGroup(47);
 
Copy content gap:G := AlternatingGroup(47);
 
Copy content sage:G = AlternatingGroup(47)
 
Copy content comment:Define the group as a permutation group
 

Group information

Description:$A_{47}$
Order: \(129\!\cdots\!000\)\(\medspace = 2^{41} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47 \)
Copy content comment:Order of the group
 
Copy content magma:Order(G);
 
Copy content gap:Order(G);
 
Copy content sage:G.order()
 
Copy content sage_gap:G.Order()
 
Exponent: \(442\!\cdots\!200\)\(\medspace = 2^{5} \cdot 3^{3} \cdot 5^{2} \cdot 7 \cdot 11 \cdot 13 \cdot 17 \cdot 19 \cdot 23 \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47 \)
Copy content comment:Exponent of the group
 
Copy content magma:Exponent(G);
 
Copy content gap:Exponent(G);
 
Copy content sage:G.exponent()
 
Copy content sage_gap:G.Exponent()
 
Automorphism group:Group of order \(258\!\cdots\!000\)\(\medspace = 2^{42} \cdot 3^{21} \cdot 5^{10} \cdot 7^{6} \cdot 11^{4} \cdot 13^{3} \cdot 17^{2} \cdot 19^{2} \cdot 23^{2} \cdot 29 \cdot 31 \cdot 37 \cdot 41 \cdot 43 \cdot 47 \)
Copy content comment:Automorphism group
 
Copy content gap:AutomorphismGroup(G);
 
Copy content magma:AutomorphismGroup(G);
 
Copy content sage_gap:G.AutomorphismGroup()
 
Composition factors:$A_{47}$
Copy content comment:Composition factors of the group
 
Copy content magma:CompositionFactors(G);
 
Copy content gap:CompositionSeries(G);
 
Copy content sage:G.composition_series()
 
Copy content sage_gap:G.CompositionSeries()
 
Derived length:$0$
Copy content comment:Derived length of the group
 
Copy content magma:DerivedLength(G);
 
Copy content gap:DerivedLength(G);
 
Copy content sage_gap:G.DerivedLength()
 

This group is nonabelian and simple (hence nonsolvable, perfect, quasisimple, and almost simple).

Copy content comment:Determine if the group G is abelian
 
Copy content magma:IsAbelian(G);
 
Copy content gap:IsAbelian(G);
 
Copy content sage:G.is_abelian()
 
Copy content sage_gap:G.IsAbelian()
 
Copy content comment:Determine if the group G is cyclic
 
Copy content magma:IsCyclic(G);
 
Copy content gap:IsCyclic(G);
 
Copy content sage:G.is_cyclic()
 
Copy content sage_gap:G.IsCyclic()
 
Copy content comment:Determine if the group G is nilpotent
 
Copy content magma:IsNilpotent(G);
 
Copy content gap:IsNilpotentGroup(G);
 
Copy content sage:G.is_nilpotent()
 
Copy content sage_gap:G.IsNilpotentGroup()
 
Copy content comment:Determine if the group G is solvable
 
Copy content magma:IsSolvable(G);
 
Copy content gap:IsSolvableGroup(G);
 
Copy content sage:G.is_solvable()
 
Copy content sage_gap:G.IsSolvableGroup()
 
Copy content comment:Determine if the group G is supersolvable
 
Copy content gap:IsSupersolvableGroup(G);
 
Copy content sage:G.is_supersolvable()
 
Copy content sage_gap:G.IsSupersolvableGroup()
 
Copy content comment:Determine if the group G is simple
 
Copy content magma:IsSimple(G);
 
Copy content gap:IsSimpleGroup(G);
 
Copy content sage_gap:G.IsSimpleGroup()
 

Group statistics

Copy content comment:Compute statistics for the group G
 
Copy content magma:// Magma code to output the first two rows of the group statistics table element_orders := [Order(g) : g in G]; orders := Set(element_orders); printf "Orders: %o\n", orders; printf "Elements: %o %o\n", [#[x : x in element_orders | x eq n] : n in orders], Order(G); cc_orders := [cc[1] : cc in ConjugacyClasses(G)]; printf "Conjugacy classes: %o %o\n", [#[x : x in cc_orders | x eq n] : n in orders], #cc_orders;
 
Copy content gap:# Gap code to output the first two rows of the group statistics table element_orders := List(Elements(G), g -> Order(g)); orders := Set(element_orders); Print("Orders: ", orders, "\n"); element_counts := List(orders, n -> Length(Filtered(element_orders, x -> x = n))); Print("Elements: ", element_counts, " ", Size(G), "\n"); cc_orders := List(ConjugacyClasses(G), cc -> Order(Representative(cc))); cc_counts := List(orders, n -> Length(Filtered(cc_orders, x -> x = n))); Print("Conjugacy classes: ", cc_counts, " ", Length(ConjugacyClasses(G)), "\n");
 
Copy content sage:# Sage code to output the first two rows of the group statistics table element_orders = [g.order() for g in G] orders = sorted(list(set(element_orders))) print("Orders:", orders) print("Elements:", [element_orders.count(n) for n in orders], G.order()) cc_orders = [cc[0].order() for cc in G.conjugacy_classes()] print("Conjugacy classes:", [cc_orders.count(n) for n in orders], len(cc_orders))
 

Order 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 50 51 52 54 55 56 57 58 60 62 63 65 66 68 69 70 72 74 75 76 77 78 80 82 84 85 86 87 88 90 91 92 93 95 96 99 100 102 104 105 108 110 111 112 114 115 116 117 119 120 123 124 126 129 130 132 133 135 136 138 140 143 144 145 148 150 152 153 154 155 156 160 161 164 165 168 170 171 174 175 176 180 182 184 185 186 187 189 190 195 198 200 203 204 205 207 208 209 210 216 217 220 221 222 224 225 228 230 231 232 234 238 240 247 248 252 253 255 259 260 261 264 266 270 272 273 275 276 279 280 285 286 288 290 296 297 299 300 304 306 308 310 312 315 319 322 323 325 330 333 336 340 341 342 345 348 350 351 352 357 360 364 368 370 372 374 377 378 380 385 390 391 396 399 400 403 406 408 414 416 418 420 425 429 432 434 435 437 440 442 444 450 455 456 459 460 462 464 465 468 475 476 480 483 493 494 495 504 506 510 513 520 522 525 528 532 540 546 550 552 555 558 560 561 570 572 580 585 594 595 598 600 609 612 616 620 624 627 630 638 644 646 650 651 660 663 665 672 680 682 684 690 693 696 700 702 714 715 720 728 741 744 748 754 756 759 760 765 770 777 780 782 792 798 805 812 816 819 825 828 836 840 850 855 858 868 870 874 880 884 897 900 910 912 920 924 930 935 936 945 952 957 966 969 975 988 990 1001 1008 1012 1015 1020 1023 1035 1040 1044 1045 1050 1064 1071 1080 1085 1092 1100 1104 1105 1116 1120 1122 1131 1140 1144 1155 1160 1170 1173 1188 1190 1196 1197 1200 1209 1218 1224 1232 1235 1240 1254 1260 1265 1275 1276 1287 1288 1292 1300 1302 1305 1309 1311 1320 1326 1330 1360 1365 1368 1380 1386 1395 1400 1404 1425 1428 1430 1449 1456 1463 1482 1485 1495 1496 1512 1518 1520 1530 1540 1547 1560 1564 1575 1584 1595 1596 1610 1615 1624 1638 1650 1656 1672 1680 1683 1705 1710 1716 1729 1740 1755 1768 1771 1785 1794 1800 1820 1827 1840 1848 1860 1870 1872 1881 1885 1890 1904 1914 1925 1932 1938 1950 1953 1955 1976 1980 1989 1995 2002 2024 2030 2040 2070 2079 2090 2093 2100 2128 2142 2145 2170 2184 2185 2200 2210 2223 2233 2244 2261 2275 2277 2280 2288 2310 2340 2346 2380 2392 2394 2415 2431 2436 2448 2457 2470 2475 2508 2520 2530 2574 2584 2604 2610 2618 2640 2652 2660 2691 2717 2730 2736 2737 2760 2772 2805 2856 2860 2898 2907 2925 2926 2964 2970 2990 2992 3003 3036 3045 3060 3080 3094 3120 3135 3150 3192 3220 3230 3255 3276 3289 3300 3315 3366 3420 3432 3458 3465 3480 3542 3553 3570 3588 3640 3696 3705 3740 3762 3780 3795 3850 3864 3876 3900 3927 3960 3978 3990 4004 4060 4080 4095 4140 4180 4186 4200 4284 4290 4368 4389 4420 4446 4485 4488 4522 4554 4560 4620 4641 4680 4760 4788 4830 4845 4862 4940 5005 5016 5040 5060 5148 5187 5236 5304 5313 5320 5355 5434 5460 5544 5610 5712 5720 5775 5796 5852 5928 5980 5985 6006 6072 6120 6160 6188 6270 6279 6300 6384 6435 6440 6460 6545 6552 6630 6732 6783 6840 6864 6916 6930 7084 7140 7245 7280 7293 7315 7410 7480 7524 7590 7735 7854 7920 7956 7980 8008 8151 8190 8280 8360 8415 8568 8580 8645 8778 8840 8855 8892 9009 9240 9282 9360 9405 9520 9576 9660 9724 9880 9945 10010 10296 10374 10472 10710 10920 11088 11115 11220 11440 11704 11781 11970 12012 12155 12376 12540 12870 13090 13104 13167 13260 13464 13860 13923 14280 14630 14820 15015 15470 15708 15960 16380 16830 17160 17556 18018 18480 18564 19635 20020 21420 21840 21945 22440 23205 23940 24024 25740 25935 26180 27720 30030 32760 36036 39270 40040 45045 60060
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Conjugacy classes   1 11 15 66 9 317 6 125 35 124 4 1522 3 68 123 83 2 471 2 469 68 30 2 1599 5 22 12 228 1 1737 1 13 33 13 31 1251 1 11 23 485 1 815 1 89 136 6 2 561 20 14 65 43 14 246 12 4 4684 4 76 11 305 37 8 278 906 2 22 28 10 208 196 1 2101 8 1 6 101 1180 8 18 5 6 32 35 35 109 71 222 59 114 3 101 83 4 10 25 5 3021 2 8 569 2 80 737 5 21 38 50 612 4 234 3 3 76 29 17 62 3 493 12 3 1 93 1395 43 13 21 7 40 1973 42 17 2 16 3 11 31 69 204 22 2 243 2 9 27 2 1870 26 2 232 3 3 6 12 173 19 51 7 134 22 705 2 5 897 2 40 1 157 5 479 17 36 13 38 4 89 3 429 31 16 5 8 1 6 1 94 10 63 112 5 309 136 1 10 1 2 650 2 323 78 1 43 21 27 12 3 2 22 984 77 5 1 15 9 1 17 56 21 420 1 302 18 3 1 4 139 21 1 7 3015 3 16 2 3 10 1 159 6 2 18 15 93 3 29 304 1 7 193 1 38 10 12 2 4 59 458 4 193 2 105 4 16 104 26 29 198 3 40 1 2 109 8 136 30 8 41 4 9 2 32 4 81 80 5 64 7 703 1 14 2 3 3 979 6 7 4 48 1 53 62 31 8 14 2 90 8 164 52 5 4 14 1 12 4 33 23 108 2 616 1 146 62 5 4 25 24 5 19 10 1383 1 17 68 2 13 1 37 9 3 13 71 15 14 438 7 4 89 6 24 2 27 3 5 6 225 5 74 4 2 252 1 10 23 3 4 22 16 13 8 1 275 4 4 3 1 1 30 1 157 19 78 3 139 2 3 31 3 9 2 2 5 34 18 3 1 20 743 2 1 1 10 7 3 2 2 3 3 1 428 18 23 9 53 20 56 105 1 5 1 2 111 25 4 11 2 13 3 2 8 3 8 5 53 133 2 257 1 5 21 1 70 10 2 1 62 5 6 5 202 5 2 31 86 2 7 1 5 1 29 5 3 84 1 1 192 3 10 12 3 2 5 4 1 1 24 5 2 2 1 3 222 3 20 12 2 1 92 8 1 7 1 14 2 22 22 1 114 2 1 7 3 2 34 1 1 3 53 3 311 127 1 35 1 14 8 1 3 3 2 4 1 20 280 3 17 1 1 1 5 54 20 22 1 1 187 1 2 15 98 12 40 27 4 1 2 3 11 1 1 1 11 6 2 41 65 3 29 7 1 23 7 1 2 57 2 3 7 5 23 33 2 31 1 1 2 69 3 39 23 6 11 4 2 3 1 6 3 1 5 78 4 39 13 1 7 20 6 6 1 3 19 54 12 4 6 1 2 11 1 1 3 291 4 43 14 9 11 2 1 4 5 6 26 2 16 2 5 6 2 8 8 1 164 35 18 3 12 2 2 3 3 1 5 24 1 12 8 3 10 2 1 1 7 2 1 3 19 10 5 2 6 3 2 56 1 49 3 4 2 2 4 4 2 2 2 8 6 2 24 6 2 29 1 2 3 5 44 1 3 2 2 1 4 88 3 2 3 1 2 5 1 1 3 7 5 2 2 7 46 2 2 11 1 1 3 3 17 2 1 5 6 2 1 2 5 1 36 2 11 1 2 8 1 4 5 18 1 10 2 2 5 2 2 6 4 2 1 2 1 1 4 4 2 1 9 7 4 1 1 1 1 3 62494
Divisions 1 11 15 66 9 317 6 125 35 124 4 1522 3 68 123 83 2 471 2 469 68 30 2 1599 5 22 12 228 1 1737 1 13 33 13 31 1251 1 11 23 485 1 815 1 89 136 6 1 561 20 14 65 43 14 246 12 4 4684 4 76 11 305 37 8 278 906 2 22 28 10 208 196 1 2101 8 1 6 101 1180 8 18 5 6 32 35 35 109 71 221 59 114 3 101 83 4 10 25 5 3021 2 8 569 1 80 737 5 21 38 50 612 4 234 3 3 76 29 17 62 3 493 12 3 1 93 1395 43 13 21 7 40 1973 42 17 2 16 3 10 31 68 204 22 2 243 1 9 27 2 1870 26 2 232 3 3 6 12 173 19 51 7 134 22 705 2 5 897 2 40 1 157 5 479 17 36 13 37 4 89 3 429 31 16 5 8 1 5 1 94 10 63 112 5 309 135 1 10 1 2 650 1 323 78 1 43 20 27 12 3 2 22 984 77 5 1 15 9 1 17 56 20 420 1 302 17 3 1 4 139 21 1 7 3015 2 15 2 3 9 1 159 6 2 18 15 93 2 29 304 1 6 193 1 38 10 11 1 4 58 458 4 193 1 105 4 14 104 26 29 198 3 40 1 2 109 8 136 30 8 41 4 9 2 32 4 81 80 5 64 7 703 1 14 2 3 3 979 6 7 4 48 1 53 62 31 8 14 2 90 8 164 52 5 4 14 1 12 4 33 22 108 1 616 1 146 62 5 4 25 23 5 19 10 1383 1 16 68 2 13 1 37 9 3 13 71 15 14 438 7 4 89 6 24 2 27 3 4 6 225 5 74 4 2 252 1 9 23 3 4 22 16 12 8 1 275 4 4 3 1 1 30 1 157 19 76 3 139 2 3 31 3 9 2 1 5 34 18 3 1 20 743 2 1 1 10 7 3 2 2 2 3 1 428 18 23 9 52 20 56 105 1 5 1 1 111 25 4 11 2 13 2 2 8 3 8 5 53 133 2 257 1 4 21 1 70 10 2 1 62 5 6 5 202 5 1 31 86 2 7 1 5 1 27 5 3 84 1 1 192 3 10 12 3 1 5 4 1 1 24 5 2 1 1 3 222 3 19 12 2 1 92 8 1 7 1 14 2 22 21 1 114 1 1 7 3 1 34 1 1 2 53 3 311 127 1 35 1 14 8 1 3 3 1 4 1 20 280 3 17 1 1 1 5 54 20 22 1 1 187 1 1 15 98 11 40 27 4 1 1 3 11 1 1 1 11 6 2 41 65 3 29 7 1 23 7 1 1 57 1 3 7 5 23 33 2 29 1 1 1 69 3 39 23 5 11 4 2 3 1 6 3 1 5 78 4 39 13 1 7 19 6 6 1 3 19 54 12 4 6 1 2 11 1 1 3 291 4 43 14 9 11 2 1 4 5 6 26 2 16 2 5 6 2 8 8 1 164 35 18 3 12 1 2 3 3 1 5 24 1 12 8 3 10 1 1 1 7 2 1 3 19 10 5 1 6 3 2 56 1 49 2 4 2 2 4 4 2 2 2 8 6 2 24 6 1 29 1 2 3 5 44 1 3 2 1 1 4 88 3 2 2 1 2 5 1 1 2 7 5 2 2 7 46 2 1 11 1 1 2 3 17 1 1 5 6 2 1 1 5 1 36 1 11 1 2 7 1 4 5 18 1 10 2 2 5 2 2 6 4 2 1 2 1 1 4 4 1 1 9 7 4 1 1 1 1 3 62419
Autjugacy classes 1 11 15 66 9 317 6 125 35 124 4 1522 3 68 123 83 2 471 2 469 68 30 2 1599 5 22 12 228 1 1737 1 13 32 13 30 1251 1 11 23 485 1 815 1 89 136 6 1 561 20 14 65 43 14 246 12 4 4684 4 76 11 305 37 8 278 906 2 22 28 10 208 196 1 2101 8 1 6 101 1180 8 18 5 6 32 35 35 109 71 221 59 114 3 101 83 4 10 25 5 3021 2 8 569 1 80 737 5 20 38 50 612 4 234 3 3 76 29 17 62 3 493 12 3 1 93 1395 43 13 21 7 40 1973 42 17 2 16 3 10 31 68 204 22 2 243 1 9 27 2 1870 26 2 232 3 3 6 12 173 19 51 7 134 22 705 2 5 897 2 40 1 157 5 479 17 36 13 37 4 89 3 429 31 16 5 8 1 5 1 94 10 63 112 5 309 135 1 10 1 2 650 1 323 78 1 43 20 27 12 3 2 22 984 77 5 1 15 9 1 17 56 20 420 1 302 17 3 1 4 139 21 1 7 3015 2 15 2 3 9 1 159 6 2 18 15 93 2 29 304 1 6 193 1 38 10 11 1 4 58 458 4 193 1 105 4 14 104 26 29 198 3 40 1 2 109 8 136 30 8 41 4 9 2 32 4 81 80 5 64 7 703 1 14 2 3 3 979 6 7 4 48 1 53 62 31 8 14 2 90 8 164 52 5 4 14 1 12 4 33 22 108 1 616 1 146 62 5 4 25 23 5 19 10 1383 1 16 68 2 13 1 37 9 3 13 71 15 14 438 7 4 89 6 24 2 27 3 4 6 225 5 74 4 2 252 1 9 23 3 4 22 16 12 8 1 275 4 4 3 1 1 30 1 157 19 76 3 139 2 3 31 3 9 2 1 5 34 18 3 1 20 743 2 1 1 10 7 3 2 2 2 3 1 428 18 23 9 52 20 56 105 1 5 1 1 111 25 4 11 2 13 2 2 8 3 8 5 53 133 2 257 1 4 21 1 70 10 2 1 62 5 6 5 202 5 1 31 86 2 7 1 5 1 27 5 3 84 1 1 192 3 10 12 3 1 5 4 1 1 24 5 2 1 1 3 222 3 19 12 2 1 92 8 1 7 1 14 2 22 21 1 114 1 1 7 3 1 34 1 1 2 53 3 311 127 1 35 1 14 8 1 3 3 1 4 1 20 280 3 17 1 1 1 5 54 20 22 1 1 187 1 1 15 98 11 40 27 4 1 1 3 11 1 1 1 11 6 2 41 65 3 29 7 1 23 7 1 1 57 1 3 7 5 23 33 2 29 1 1 1 69 3 39 23 5 11 4 2 3 1 6 3 1 5 78 4 39 13 1 7 19 6 6 1 3 19 54 12 4 6 1 2 11 1 1 3 291 4 43 14 9 11 2 1 4 5 6 26 2 16 2 5 6 2 8 8 1 164 35 18 3 12 1 2 3 3 1 5 24 1 12 8 3 10 1 1 1 7 2 1 3 19 10 5 1 6 3 2 56 1 49 2 4 2 2 4 4 2 2 2 8 6 2 24 6 1 29 1 2 3 5 44 1 3 2 1 1 4 88 3 2 2 1 2 5 1 1 2 7 5 2 2 7 46 2 1 11 1 1 2 3 17 1 1 5 6 2 1 1 5 1 36 1 11 1 2 7 1 4 5 18 1 10 2 2 5 2 2 6 4 2 1 2 1 1 4 4 1 1 9 7 4 1 1 1 1 3 62416

Minimal presentations

Permutation degree:$47$
Transitive degree:not computed
Rank: $2$
Inequivalent generating pairs: not computed

Minimal degrees of linear representations for this group have not been computed

Constructions

Show commands: Gap / Magma / SageMath


Permutation group:Degree $47$ $\langle(1,2,3), (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)\rangle$ Copy content Toggle raw display
Copy content comment:Define the group as a permutation group
 
Copy content magma:G := PermutationGroup< 47 | (1,2,3), (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47) >;
 
Copy content gap:G := Group( (1,2,3), (3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47) );
 
Copy content sage:G = PermutationGroup(['(1,2,3)', '(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)'])
 
Transitive group: 47T5 more information
Direct product: not isomorphic to a non-trivial direct product
Semidirect product: not isomorphic to a non-trivial semidirect product
Trans. wreath product: not isomorphic to a non-trivial transitive wreath product

Elements of the group are displayed as permutations of degree 47.

Homology

Abelianization: $C_1 $
Copy content comment:The abelianization of the group
 
Copy content magma:quo< G | CommutatorSubgroup(G) >;
 
Copy content gap:FactorGroup(G, DerivedSubgroup(G));
 
Copy content sage:G.quotient(G.commutator())
 
Schur multiplier: not computed
Copy content comment:The Schur multiplier of the group
 
Copy content gap:AbelianInvariantsMultiplier(G);
 
Copy content sage:G.homology(2)
 
Copy content sage_gap:G.AbelianInvariantsMultiplier()
 
Commutator length: not computed
Copy content comment:The commutator length of the group
 
Copy content gap:CommutatorLength(G);
 
Copy content sage_gap:G.CommutatorLength()
 

Subgroups

Copy content comment:List of subgroups of the group
 
Copy content magma:Subgroups(G);
 
Copy content gap:AllSubgroups(G);
 
Copy content sage:G.subgroups()
 
Copy content sage_gap:G.AllSubgroups()
 

Subgroup data has not been computed.

Character theory

Copy content comment:Character table
 
Copy content magma:CharacterTable(G); // Output not guaranteed to exactly match the LMFDB table
 
Copy content gap:CharacterTable(G); # Output not guaranteed to exactly match the LMFDB table
 
Copy content sage:G.character_table() # Output not guaranteed to exactly match the LMFDB table
 
Copy content sage_gap:G.CharacterTable() # Output not guaranteed to exactly match the LMFDB table
 

Complex character table

The $62494 \times 62494$ character table is not available for this group.

Rational character table

The $62419 \times 62419$ rational character table is not available for this group.