Finite Group DatabasebetaFinite Group Databasebeta| order | 23025 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×C307⋊C3 |
| unambiguous semidirect product | C307⋊(C3×C52) |
| unambiguous semidirect product | (C5×C307)⋊(C3×C5) |
| Fitting, socle, Hall | C52×C307 ⋊ C3 |
| derived, Sylow | C307 ⋊ C3×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C307⋊C3 |
| commutator, cosocle, hypocenter | C307 | C3×C52 |
| Frattini | C1 | G |
| Fitting, socle | C52×C307 | C3 |
| LCS | G ▷ C307 | |
| UCS | C1 ◁ C52 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7675 |
2625 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23025, 6);