Finite Group DatabasebetaFinite Group Databasebeta| order | 31164 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C7 |
| abelian | C3×C4×C72×C53 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C2 | C2×C3×C72×C53 |
| socle, prime radical | C2×C3×C72×C53 | C2 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
120 conjugacy classes of subgroups.
| minimal degree | μ(G) = 74 |
| transitive degree | μt(G) = 31164 |
A minimal faithful permutation representation — 2 generators on 74 points:
(1,2,3,4)(5,6,7)(8,9,10,11,12,13,14)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74);(15,16,17,18,19,20,21)31164 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31164, 41);