Finite Group DatabasebetaFinite Group Databasebeta| order | 31974 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C732 ⋊ C2×C3 |
| Hall | #30630500 ⋊ C2 |
| Hall | C73⋊D73 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C732 | C2×C3 |
| LCS | G ▷ C732 | |
| UCS | C1 | |
304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 146 |
| transitive degree | μt(G) = 5329 |
A minimal faithful permutation representation — 3 generators on 146 points:
(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,60)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,48,57,34,49,63)(37,42,62,50,51,58)(40,67,65,54,55,53)(52,61,68,56,64,72)(59,73,71,69,70,66)(75,79,80,76,77,81)(78,87,88,82,83,97)(84,100,101,90,91,114)(85,99,95,93,89,86)(92,119,120,103,104,133)(94,117,118,106,102,111)(96,98,116,108,109,112)(105,121,130,107,122,136)(110,115,135,123,124,131)(113,140,138,127,128,126)(125,134,141,129,137,145)(132,146,144,142,143,139);(74,75,78,84,92,105,106,93,77,81,86,96,110,125,127,109,83,89,97,111,126,139,142,124,91,102,112,114,130,141,146,137,104,121,128,131,133,120,135,140,122,119,134,143,145,136,101,116,117,100,115,132,144,138,118,88,99,87,98,113,129,123,108,95,80,79,85,94,107,103,90,82,76);(1,2,5,11,19,32,33,20,4,8,13,23,37,52,54,36,10,16,24,38,53,66,69,51,18,29,39,41,57,68,73,64,31,48,55,58,60,47,62,67,49,46,61,70,72,63,28,43,44,27,42,59,71,65,45,15,26,14,25,40,56,50,35,22,7,6,12,21,34,30,17,9,3)Polycyclic presentation:
2,3,73^2|c^a=c^72,d^a=d^72,c^b=c^8,d^b=d^8894 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31974, 12);