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Order Exponent Nilpotency class Nilpotent
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Results (1-50 of 211 matches)

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Label Name Family name Order Exponent $\card{\mathrm{conj}(G)}$ Center Central quotient Commutator Abelianization Type - length
2.1 $C_2$ $\GSOPlus(2,2)$ $2$ $2$ 2 $C_2$ $C_1$ $C_1$ $C_{2}$ Cyclic
4.1 $C_4$ $\GSOPlus(2,3)$ $2^{2}$ $2^{2}$ 4 $C_4$ $C_1$ $C_1$ $C_{4}$ Cyclic
6.1 $S_3$ $\GSOPlus(2,4)$ $2 \cdot 3$ $2 \cdot 3$ 3 $C_1$ $S_3$ $C_3$ $C_{2}$ Solvable - 2
8.4 $Q_8$ $\GSOPlus(2,5)$ $2^{3}$ $2^{2}$ 5 $C_2$ $C_2^2$ $C_2$ $C_{2}^{2}$ Nilpotent - 2
12.1 $C_3:C_4$ $\GSOPlus(2,7)$ $2^{2} \cdot 3$ $2^{2} \cdot 3$ 6 $C_2$ $S_3$ $C_3$ $C_{4}$ Solvable - 2
14.1 $D_7$ $\GSOPlus(2,8)$ $2 \cdot 7$ $2 \cdot 7$ 5 $C_1$ $D_7$ $C_7$ $C_{2}$ Solvable - 2
16.9 $Q_{16}$ $\GSOPlus(2,9)$ $2^{4}$ $2^{3}$ 7 $C_2$ $D_4$ $C_4$ $C_{2}^{2}$ Nilpotent - 3
20.1 $C_5:C_4$ $\GSOPlus(2,11)$ $2^{2} \cdot 5$ $2^{2} \cdot 5$ 8 $C_2$ $D_5$ $C_5$ $C_{4}$ Solvable - 2
24.4 $C_3:Q_8$ $\GSOPlus(2,13)$ $2^{3} \cdot 3$ $2^{2} \cdot 3$ 9 $C_2$ $D_6$ $C_6$ $C_{2}^{2}$ Solvable - 2
30.3 $D_{15}$ $\GSOPlus(2,16)$ $2 \cdot 3 \cdot 5$ $2 \cdot 3 \cdot 5$ 9 $C_1$ $D_{15}$ $C_{15}$ $C_{2}$ Solvable - 2
32.20 $Q_{32}$ $\GSOPlus(2,17)$ $2^{5}$ $2^{4}$ 11 $C_2$ $D_8$ $C_8$ $C_{2}^{2}$ Nilpotent - 4
36.1 $C_9:C_4$ $\GSOPlus(2,19)$ $2^{2} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 12 $C_2$ $D_9$ $C_9$ $C_{4}$ Solvable - 2
44.1 $C_{11}:C_4$ $\GSOPlus(2,23)$ $2^{2} \cdot 11$ $2^{2} \cdot 11$ 14 $C_2$ $D_{11}$ $C_{11}$ $C_{4}$ Solvable - 2
48.8 $C_3:Q_{16}$ $\GSOPlus(2,25)$ $2^{4} \cdot 3$ $2^{3} \cdot 3$ 15 $C_2$ $D_{12}$ $C_{12}$ $C_{2}^{2}$ Solvable - 2
52.1 $C_{13}:C_4$ $\GSOPlus(2,27)$ $2^{2} \cdot 13$ $2^{2} \cdot 13$ 16 $C_2$ $D_{13}$ $C_{13}$ $C_{4}$ Solvable - 2
56.3 $C_7:Q_8$ $\GSOPlus(2,29)$ $2^{3} \cdot 7$ $2^{2} \cdot 7$ 17 $C_2$ $D_{14}$ $C_{14}$ $C_{2}^{2}$ Solvable - 2
60.3 $C_{15}:C_4$ $\GSOPlus(2,31)$ $2^{2} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 18 $C_2$ $D_{15}$ $C_{15}$ $C_{4}$ Solvable - 2
62.1 $D_{31}$ $\GSOPlus(2,32)$ $2 \cdot 31$ $2 \cdot 31$ 17 $C_1$ $D_{31}$ $C_{31}$ $C_{2}$ Solvable - 2
72.4 $C_9:Q_8$ $\GSOPlus(2,37)$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3^{2}$ 21 $C_2$ $D_{18}$ $C_{18}$ $C_{2}^{2}$ Solvable - 2
72.40 $\SOPlus(4,2)$ $\GSOPlus(4,2)$ $2^{3} \cdot 3^{2}$ $2^{2} \cdot 3$ 9 $C_1$ $\SOPlus(4,2)$ $C_3:S_3$ $C_{2}^{2}$ Solvable - 3
80.8 $C_5:Q_{16}$ $\GSOPlus(2,41)$ $2^{4} \cdot 5$ $2^{3} \cdot 5$ 23 $C_2$ $D_{20}$ $C_{20}$ $C_{2}^{2}$ Solvable - 2
84.5 $C_{21}:C_4$ $\GSOPlus(2,43)$ $2^{2} \cdot 3 \cdot 7$ $2^{2} \cdot 3 \cdot 7$ 24 $C_2$ $D_{21}$ $C_{21}$ $C_{4}$ Solvable - 2
92.1 $C_{23}:C_4$ $\GSOPlus(2,47)$ $2^{2} \cdot 23$ $2^{2} \cdot 23$ 26 $C_2$ $D_{23}$ $C_{23}$ $C_{4}$ Solvable - 2
96.8 $C_3:Q_{32}$ $\GSOPlus(2,49)$ $2^{5} \cdot 3$ $2^{4} \cdot 3$ 27 $C_2$ $D_{24}$ $C_{24}$ $C_{2}^{2}$ Solvable - 2
104.4 $C_{13}:Q_8$ $\GSOPlus(2,53)$ $2^{3} \cdot 13$ $2^{2} \cdot 13$ 29 $C_2$ $D_{26}$ $C_{26}$ $C_{2}^{2}$ Solvable - 2
116.1 $C_{29}:C_4$ $\GSOPlus(2,59)$ $2^{2} \cdot 29$ $2^{2} \cdot 29$ 32 $C_2$ $D_{29}$ $C_{29}$ $C_{4}$ Solvable - 2
120.26 $C_{15}:Q_8$ $\GSOPlus(2,61)$ $2^{3} \cdot 3 \cdot 5$ $2^{2} \cdot 3 \cdot 5$ 33 $C_2$ $D_{30}$ $C_{30}$ $C_{2}^{2}$ Solvable - 2
126.5 $D_{63}$ $\GSOPlus(2,64)$ $2 \cdot 3^{2} \cdot 7$ $2 \cdot 3^{2} \cdot 7$ 33 $C_1$ $D_{63}$ $C_{63}$ $C_{2}$ Solvable - 2
132.3 $C_{33}:C_4$ $\GSOPlus(2,67)$ $2^{2} \cdot 3 \cdot 11$ $2^{2} \cdot 3 \cdot 11$ 36 $C_2$ $D_{33}$ $C_{33}$ $C_{4}$ Solvable - 2
140.3 $C_{35}:C_4$ $\GSOPlus(2,71)$ $2^{2} \cdot 5 \cdot 7$ $2^{2} \cdot 5 \cdot 7$ 38 $C_2$ $D_{35}$ $C_{35}$ $C_{4}$ Solvable - 2
144.4 $C_9:Q_{16}$ $\GSOPlus(2,73)$ $2^{4} \cdot 3^{2}$ $2^{3} \cdot 3^{2}$ 39 $C_2$ $D_{36}$ $C_{36}$ $C_{2}^{2}$ Solvable - 2
156.5 $C_{39}:C_4$ $\GSOPlus(2,79)$ $2^{2} \cdot 3 \cdot 13$ $2^{2} \cdot 3 \cdot 13$ 42 $C_2$ $D_{39}$ $C_{39}$ $C_{4}$ Solvable - 2
160.8 $C_5:Q_{32}$ $\GSOPlus(2,81)$ $2^{5} \cdot 5$ $2^{4} \cdot 5$ 43 $C_2$ $D_{40}$ $C_{40}$ $C_{2}^{2}$ Solvable - 2
164.1 $C_{41}:C_4$ $\GSOPlus(2,83)$ $2^{2} \cdot 41$ $2^{2} \cdot 41$ 44 $C_2$ $D_{41}$ $C_{41}$ $C_{4}$ Solvable - 2
176.7 $C_{11}:Q_{16}$ $\GSOPlus(2,89)$ $2^{4} \cdot 11$ $2^{3} \cdot 11$ 47 $C_2$ $D_{44}$ $C_{44}$ $C_{2}^{2}$ Solvable - 2
192.9 $C_3:Q_{64}$ $\GSOPlus(2,97)$ $2^{6} \cdot 3$ $2^{5} \cdot 3$ 51 $C_2$ $D_{48}$ $C_{48}$ $C_{2}^{2}$ Solvable - 2
200.4 $C_{25}:Q_8$ $\GSOPlus(2,101)$ $2^{3} \cdot 5^{2}$ $2^{2} \cdot 5^{2}$ 53 $C_2$ $D_{50}$ $C_{50}$ $C_{2}^{2}$ Solvable - 2
204.3 $C_{51}:C_4$ $\GSOPlus(2,103)$ $2^{2} \cdot 3 \cdot 17$ $2^{2} \cdot 3 \cdot 17$ 54 $C_2$ $D_{51}$ $C_{51}$ $C_{4}$ Solvable - 2
212.1 $C_{53}:C_4$ $\GSOPlus(2,107)$ $2^{2} \cdot 53$ $2^{2} \cdot 53$ 56 $C_2$ $D_{53}$ $C_{53}$ $C_{4}$ Solvable - 2
216.4 $C_{27}:Q_8$ $\GSOPlus(2,109)$ $2^{3} \cdot 3^{3}$ $2^{2} \cdot 3^{3}$ 57 $C_2$ $D_{54}$ $C_{54}$ $C_{2}^{2}$ Solvable - 2
224.7 $C_7:Q_{32}$ $\GSOPlus(2,113)$ $2^{5} \cdot 7$ $2^{4} \cdot 7$ 59 $C_2$ $D_{56}$ $C_{56}$ $C_{2}^{2}$ Solvable - 2
240.69 $C_{15}:Q_{16}$ $\GSOPlus(2,121)$ $2^{4} \cdot 3 \cdot 5$ $2^{3} \cdot 3 \cdot 5$ 63 $C_2$ $D_{60}$ $C_{60}$ $C_{2}^{2}$ Solvable - 2
248.3 $C_{31}:Q_8$ $\GSOPlus(2,125)$ $2^{3} \cdot 31$ $2^{2} \cdot 31$ 65 $C_2$ $D_{62}$ $C_{62}$ $C_{2}^{2}$ Solvable - 2
252.5 $C_{63}:C_4$ $\GSOPlus(2,127)$ $2^{2} \cdot 3^{2} \cdot 7$ $2^{2} \cdot 3^{2} \cdot 7$ 66 $C_2$ $D_{63}$ $C_{63}$ $C_{4}$ Solvable - 2
254.1 $D_{127}$ $\GSOPlus(2,128)$ $2 \cdot 127$ $2 \cdot 127$ 65 $C_1$ $D_{127}$ $C_{127}$ $C_{2}$ Solvable - 2
260.3 $C_{65}:C_4$ $\GSOPlus(2,131)$ $2^{2} \cdot 5 \cdot 13$ $2^{2} \cdot 5 \cdot 13$ 68 $C_2$ $D_{65}$ $C_{65}$ $C_{4}$ Solvable - 2
272.8 $C_{17}:Q_{16}$ $\GSOPlus(2,137)$ $2^{4} \cdot 17$ $2^{3} \cdot 17$ 71 $C_2$ $D_{68}$ $C_{68}$ $C_{2}^{2}$ Solvable - 2
276.3 $C_{69}:C_4$ $\GSOPlus(2,139)$ $2^{2} \cdot 3 \cdot 23$ $2^{2} \cdot 3 \cdot 23$ 72 $C_2$ $D_{69}$ $C_{69}$ $C_{4}$ Solvable - 2
296.4 $C_{37}:Q_8$ $\GSOPlus(2,149)$ $2^{3} \cdot 37$ $2^{2} \cdot 37$ 77 $C_2$ $D_{74}$ $C_{74}$ $C_{2}^{2}$ Solvable - 2
300.3 $C_{75}:C_4$ $\GSOPlus(2,151)$ $2^{2} \cdot 3 \cdot 5^{2}$ $2^{2} \cdot 3 \cdot 5^{2}$ 78 $C_2$ $D_{75}$ $C_{75}$ $C_{4}$ Solvable - 2
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