Finite Group DatabasebetaFinite Group Databasebeta| order | 31213 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C76 |
| abelian | C74×C13 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
7304 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 31213 |
A minimal faithful permutation representation — 4 generators on 41 points:
(1,2,3,4,5,6,7)(29,30,31,32,33,34,35,36,37,38,39,40,41);(8,9,10,11,12,13,14);(15,16,17,18,19,20,21);(22,23,24,25,26,27,28)31213 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(31213, 15);