Finite Group DatabasebetaFinite Group Databasebeta| order | 31974 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, Sylow | C732 ⋊ D3 |
| derived, Hall | #30630501 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | #30630501 | C2 |
| Fitting, socle | C732 | D3 |
| LCS | G ▷ #30630501 | |
| UCS | C1 | |
25 conjugacy classes of subgroups.
| minimal degree | μ(G) = 146 |
| transitive degree | μt(G) = 146 |
A minimal faithful permutation representation — 2 generators on 146 points:
(1,7,18,28,56,73,112,126,105,141,79,125,53,98,33,70,19,44,10,15,36,48,86,101,135,142,131,146,109,140,83,124,57,76,37,68,22,29,60,74,115,128,145,143,144,129,132,103,106,50,67,122,61,95,40,49,89,102,137,133,134,107,110,77,80,30,43,96,116,139,90,121,64,75,118,111,113,81,84,51,54,16,25,69,104,123,138,136,119,114,93,85,87,55,58,31,34,8,13,45,78,97,130,117,120,88,91,59,62,35,38,17,20,4,6,27,52,71,108,92,94,63,65,39,41,21,23,9,11,2,3,14,32,47,82,99,66,127,42,100,24,72,12,46,5,26);(3,5,10)(4,7,9)(6,12,22)(8,15,21)(11,19,18)(13,24,40)(14,26,17)(16,29,39)(20,33,36)(23,37,32)(25,42,64)(27,44,35)(28,46,31)(30,49,63)(34,53,60)(38,57,56)(41,61,52)(43,66,93)(45,68,59)(47,70,55)(48,72,51)(50,75,92)(54,79,89)(58,83,86)(62,67,82)(65,90,78)(69,95,88)(71,76,85)(73,98,81)(74,100,77)(80,105,118)(84,109,115)(87,106,112)(91,116,108)(94,119,104)(96,121,117)(97,122,114)(99,124,111)(101,125,107)(102,127,103)(110,131,137)(113,132,135)(120,138,130)(123,139,136)(126,140,133)(128,141,129)(134,144,145)(142,146,143)Polycyclic presentation:
2,3,73^2|b^a=b^2,c^a=d,d^a=c,c^b=c^64,d^b=d^8999 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31974, 8);