Finite Group DatabasebetaFinite Group Databasebeta| order | 32340 |
| automorphism | ? |
| homology | Abelianization (H1) = C72×C11 · Schur multiplier (H2) = C2×C7 |
| direct product | C72×C11×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C72×C11 | A5 |
| commutator, hypocenter | A5 | C72×C11 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C72×C11 | |
180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 30 |
| transitive degree | μt(G) = 2695 |
A minimal faithful permutation representation — 2 generators on 30 points:
(1,2,3,4,5,6,7)(8,9,11,13,10,12,14)(26,27,28,29,30);(8,10,9,12,11,14,13)(15,16,17,18,19,20,21,22,23,24,25)(26,27,29,28,30)2695 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32340, 658);