Finite Group DatabasebetaFinite Group Databasebeta| order | 23100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52⋊C3×D77 |
| unambiguous semidirect product | (C2×C11)⋊(D7×C52⋊C3) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C52⋊C3×D77 |
| commutator, cosocle, hypocenter | C52×C7×C11 | C22×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7×C11 | C2×C3 |
| LCS | G ▷ C52×C7×C11 | |
| UCS | C1 ◁ C2 | |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2310 |
880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23100, 389);