Finite Group DatabasebetaFinite Group Databasebeta| order | 23604 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C3×#11765499⋊C7 |
| unambiguous semidirect product | #11765499⋊(C3×C7) |
| unambiguous semidirect product | (C3×#11765499)⋊C7 |
| Fitting, socle, Hall | C3×C281 ⋊ C4×C7 |
| derived, Sylow | C281 ⋊ C3×C4×C7 |
| Hall | C3×C281⋊C7 ⋊ C4 |
| Hall | C3×#11765499 ⋊ C7 |
| Hall | C281⋊C7 ⋊ C3×C4 |
| Hall | #11765499 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #11765499⋊C7 |
| commutator, hypocenter | C281 | C3×C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C281 | C4×C7 |
| prime radical | C3×D281⋊C7 | C2 |
| cosocle | D281 | C2×C3×C7 |
| LCS | G ▷ C281 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 843 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23604, 18);