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Group invariants
| Abstract group: | $C_{11}^2:D_{10}$ |
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| Order: | $2420=2^{2} \cdot 5 \cdot 11^{2}$ |
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| Cyclic: | no |
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| Abelian: | no |
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| Solvable: | yes |
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| Nilpotency class: | not nilpotent |
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Group action invariants
| Degree $n$: | $22$ |
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| Transitive number $t$: | $17$ |
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| Parity: | $-1$ |
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| Primitive: | no |
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| $\card{\Aut(F/K)}$: | $1$ |
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| Generators: | $(1,8,11,6,7,9,2,10,4,3)(12,21,20,14,22,15,17,18,13,16)$, $(1,16,6,20,11,13,5,17,10,21,4,14,9,18,3,22,8,15,2,19,7,12)$ |
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Low degree resolvents
$\card{(G/N)}$ Galois groups for stem field(s) $2$: $C_2$ x 3 $4$: $C_2^2$ $10$: $D_{5}$ $20$: $D_{10}$ Resolvents shown for degrees $\leq 47$
Subfields
Degree 2: $C_2$
Degree 11: None
Low degree siblings
44T61Siblings are shown with degree $\leq 47$
A number field with this Galois group has no arithmetically equivalent fields.
Conjugacy classes
| Label | Cycle Type | Size | Order | Index | Representative |
| 1A | $1^{22}$ | $1$ | $1$ | $0$ | $()$ |
| 2A | $2^{11}$ | $55$ | $2$ | $11$ | $( 1,12)( 2,19)( 3,15)( 4,22)( 5,18)( 6,14)( 7,21)( 8,17)( 9,13)(10,20)(11,16)$ |
| 2B | $2^{11}$ | $55$ | $2$ | $11$ | $( 1,16)( 2,17)( 3,18)( 4,19)( 5,20)( 6,21)( 7,22)( 8,12)( 9,13)(10,14)(11,15)$ |
| 2C | $2^{10},1^{2}$ | $121$ | $2$ | $10$ | $( 1, 9)( 2, 8)( 3, 7)( 4, 6)(10,11)(12,21)(13,20)(14,19)(15,18)(16,17)$ |
| 5A1 | $5^{4},1^{2}$ | $242$ | $5$ | $16$ | $( 1, 2,11, 4, 7)( 3, 9, 8,10, 6)(12,16,14,15,20)(13,21,17,19,18)$ |
| 5A2 | $5^{4},1^{2}$ | $242$ | $5$ | $16$ | $( 1,11, 7, 2, 4)( 3, 8, 6, 9,10)(12,14,20,16,15)(13,17,18,21,19)$ |
| 10A1 | $10^{2},1^{2}$ | $242$ | $10$ | $18$ | $( 1, 6, 2, 3,11, 9, 4, 8, 7,10)(12,18,16,13,14,21,15,17,20,19)$ |
| 10A3 | $10^{2},1^{2}$ | $242$ | $10$ | $18$ | $( 1, 3, 4,10, 2, 9, 7, 6,11, 8)(12,13,15,19,16,21,20,18,14,17)$ |
| 11A1 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,22,21,20,19,18,17,16,15,14,13)$ |
| 11A2 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 7, 2, 8, 3, 9, 4,10, 5,11, 6)(12,21,19,17,15,13,22,20,18,16,14)$ |
| 11A3 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,20,17,14,22,19,16,13,21,18,15)$ |
| 11A4 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,19,15,22,18,14,21,17,13,20,16)$ |
| 11A5 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 5, 9, 2, 6,10, 3, 7,11, 4, 8)(12,18,13,19,14,20,15,21,16,22,17)$ |
| 11B1 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1,10, 8, 6, 4, 2,11, 9, 7, 5, 3)(12,21,19,17,15,13,22,20,18,16,14)$ |
| 11B2 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 8, 4,11, 7, 3,10, 6, 2, 9, 5)(12,19,15,22,18,14,21,17,13,20,16)$ |
| 11B3 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 6,11, 5,10, 4, 9, 3, 8, 2, 7)(12,17,22,16,21,15,20,14,19,13,18)$ |
| 11B4 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)(12,15,18,21,13,16,19,22,14,17,20)$ |
| 11B5 | $11^{2}$ | $10$ | $11$ | $20$ | $( 1, 2, 3, 4, 5, 6, 7, 8, 9,10,11)(12,13,14,15,16,17,18,19,20,21,22)$ |
| 11C | $11,1^{11}$ | $20$ | $11$ | $10$ | $( 1, 4, 7,10, 2, 5, 8,11, 3, 6, 9)$ |
| 22A1 | $22$ | $110$ | $22$ | $21$ | $( 1,17, 4,16, 7,15,10,14, 2,13, 5,12, 8,22,11,21, 3,20, 6,19, 9,18)$ |
| 22A3 | $22$ | $110$ | $22$ | $21$ | $( 1,16,10,13, 8,21, 6,18, 4,15, 2,12,11,20, 9,17, 7,14, 5,22, 3,19)$ |
| 22A5 | $22$ | $110$ | $22$ | $21$ | $( 1,15, 5,21, 9,16, 2,22, 6,17,10,12, 3,18, 7,13,11,19, 4,14, 8,20)$ |
| 22A7 | $22$ | $110$ | $22$ | $21$ | $( 1,14,11,18,10,22, 9,15, 8,19, 7,12, 6,16, 5,20, 4,13, 3,17, 2,21)$ |
| 22A9 | $22$ | $110$ | $22$ | $21$ | $( 1,13, 6,15,11,17, 5,19,10,21, 4,12, 9,14, 3,16, 8,18, 2,20, 7,22)$ |
| 22B1 | $22$ | $110$ | $22$ | $21$ | $( 1,15,10,13, 8,22, 6,20, 4,18, 2,16,11,14, 9,12, 7,21, 5,19, 3,17)$ |
| 22B3 | $22$ | $110$ | $22$ | $21$ | $( 1,13, 6,18,11,12, 5,17,10,22, 4,16, 9,21, 3,15, 8,20, 2,14, 7,19)$ |
| 22B5 | $22$ | $110$ | $22$ | $21$ | $( 1,22, 2,12, 3,13, 4,14, 5,15, 6,16, 7,17, 8,18, 9,19,10,20,11,21)$ |
| 22B7 | $22$ | $110$ | $22$ | $21$ | $( 1,20, 9,17, 6,14, 3,22,11,19, 8,16, 5,13, 2,21,10,18, 7,15, 4,12)$ |
| 22B9 | $22$ | $110$ | $22$ | $21$ | $( 1,18, 5,22, 9,15, 2,19, 6,12,10,16, 3,20, 7,13,11,17, 4,21, 8,14)$ |
Malle's constant $a(G)$: $1/10$
Character table
| 1A | 2A | 2B | 2C | 5A1 | 5A2 | 10A1 | 10A3 | 11A1 | 11A2 | 11A3 | 11A4 | 11A5 | 11B1 | 11B2 | 11B3 | 11B4 | 11B5 | 11C | 22A1 | 22A3 | 22A5 | 22A7 | 22A9 | 22B1 | 22B3 | 22B5 | 22B7 | 22B9 | ||
| Size | 1 | 55 | 55 | 121 | 242 | 242 | 242 | 242 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 | 110 | 110 | 110 | 110 | 110 | 110 | 110 | 110 | 110 | 110 | |
| 2 P | 1A | 1A | 1A | 1A | 5A2 | 5A1 | 5A1 | 5A2 | 11A2 | 11A4 | 11A5 | 11A3 | 11A1 | 11B2 | 11B4 | 11B5 | 11B3 | 11B1 | 11C | 11A1 | 11A3 | 11A5 | 11A4 | 11A2 | 11B1 | 11B3 | 11B5 | 11B4 | 11B2 | |
| 5 P | 1A | 2A | 2B | 2C | 1A | 1A | 2C | 2C | 11A5 | 11A1 | 11A4 | 11A2 | 11A3 | 11B5 | 11B1 | 11B4 | 11B2 | 11B3 | 11C | 22A5 | 22A7 | 22A3 | 22A9 | 22A1 | 22B5 | 22B7 | 22B3 | 22B9 | 22B1 | |
| 11 P | 1A | 2A | 2B | 2C | 5A1 | 5A2 | 10A1 | 10A3 | 1A | 1A | 1A | 1A | 1A | 1A | 1A | 1A | 1A | 1A | 1A | 2A | 2A | 2A | 2A | 2A | 2B | 2B | 2B | 2B | 2B | |
| Type | ||||||||||||||||||||||||||||||
| 2420.bl.1a | R | |||||||||||||||||||||||||||||
| 2420.bl.1b | R | |||||||||||||||||||||||||||||
| 2420.bl.1c | R | |||||||||||||||||||||||||||||
| 2420.bl.1d | R | |||||||||||||||||||||||||||||
| 2420.bl.2a1 | R | |||||||||||||||||||||||||||||
| 2420.bl.2a2 | R | |||||||||||||||||||||||||||||
| 2420.bl.2b1 | R | |||||||||||||||||||||||||||||
| 2420.bl.2b2 | R | |||||||||||||||||||||||||||||
| 2420.bl.10a1 | R | |||||||||||||||||||||||||||||
| 2420.bl.10a2 | R | |||||||||||||||||||||||||||||
| 2420.bl.10a3 | R | |||||||||||||||||||||||||||||
| 2420.bl.10a4 | R | |||||||||||||||||||||||||||||
| 2420.bl.10a5 | R | |||||||||||||||||||||||||||||
| 2420.bl.10b1 | R | |||||||||||||||||||||||||||||
| 2420.bl.10b2 | R | |||||||||||||||||||||||||||||
| 2420.bl.10b3 | R | |||||||||||||||||||||||||||||
| 2420.bl.10b4 | R | |||||||||||||||||||||||||||||
| 2420.bl.10b5 | R | |||||||||||||||||||||||||||||
| 2420.bl.10c1 | R | |||||||||||||||||||||||||||||
| 2420.bl.10c2 | R | |||||||||||||||||||||||||||||
| 2420.bl.10c3 | R | |||||||||||||||||||||||||||||
| 2420.bl.10c4 | R | |||||||||||||||||||||||||||||
| 2420.bl.10c5 | R | |||||||||||||||||||||||||||||
| 2420.bl.10d1 | R | |||||||||||||||||||||||||||||
| 2420.bl.10d2 | R | |||||||||||||||||||||||||||||
| 2420.bl.10d3 | R | |||||||||||||||||||||||||||||
| 2420.bl.10d4 | R | |||||||||||||||||||||||||||||
| 2420.bl.10d5 | R | |||||||||||||||||||||||||||||
| 2420.bl.20a | R |
Regular extensions
Data not computed