Finite Group DatabasebetaFinite Group Databasebeta| order | 23604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(#11765499⋊C7) |
| unambiguous semidirect product | (C3⋊#11765499)⋊C7 |
| Fitting, socle, derived, Hall | C3×C281 ⋊ C4×C7 |
| Hall | C3×C281⋊C7 ⋊ C4 |
| Hall | C3⋊#11765499 ⋊ C7 |
| Hall | C281⋊C7 ⋊ Dic3 |
| Sylow | C281 ⋊ C7×Dic3 |
| Sylow | C3 ⋊ #11765499⋊C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C281 | C4×C7 |
| prime radical | C3×D281⋊C7 | C2 |
| cosocle | C3×D281 | C2×C7 |
| LCS | G ▷ C3×C281 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 843 |
Polycyclic presentation:
2,7,2,3,281|a^2=c,d^a=d^2,e^a=e^53,e^b=e^249,e^c=e^28072 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23604, 19);