Finite Group DatabasebetaFinite Group Databasebeta| order | 23604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×C3⋊#11765499 |
| unambiguous semidirect product | C3⋊(C7×#11765499) |
| Fitting, socle, Hall | C3×C7×C281 ⋊ C4 |
| derived, Hall | C3×C281 ⋊ C4×C7 |
| Hall | C7×C281 ⋊ Dic3 |
| Sylow | C281 ⋊ C7×Dic3 |
| Hall | C3×C7 ⋊ #11765499 |
| Sylow | C3 ⋊ C7×#11765499 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | C3⋊#11765499 |
| commutator, hypocenter | C3×C281 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C281 | C4 |
| prime radical | C3×C7×D281 | C2 |
| cosocle | C3×D281 | C2×C7 |
| LCS | G ▷ C3×C281 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5901 |
1512 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23604, 35);