Finite Group DatabasebetaFinite Group Databasebeta| order | 23724 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic659 |
| unambiguous semidirect product | C659⋊(C32×C4) |
| derived, Sylow | C659 ⋊ C32×C4 |
| Hall | C32×C659 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D659 |
| commutator, hypocenter | C659 | C32×C4 |
| Frattini | C2 | C32×D659 |
| Fitting, socle, prime radical | C2×C32×C659 | C2 |
| cosocle | C2×C659 | C2×C32 |
| LCS | G ▷ C659 | |
| UCS | C1 ◁ C2×C32 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23724 |
5958 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23724, 16);