Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C11 · Schur multiplier (H2) = C2 |
| direct product | C5×C7×C11×A5 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C5×C7×C11 | A5 |
| commutator, hypocenter | A5 | C5×C7×C11 |
| Frattini | C1 | G |
| LCS | G ▷ A5 | |
| UCS | C1 ◁ C5×C7×C11 | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 1925 |
A minimal faithful permutation representation — 2 generators on 28 points:
(24,28,27);(1,2,3,4,5)(6,7,8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)(24,26,25)1925 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 571);