Finite Group DatabasebetaFinite Group Databasebeta| order | 25668 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×Dic713 |
| unambiguous semidirect product | C23⋊(C32×Dic31) |
| derived, Hall | C23×C31 ⋊ C32×C4 |
| Hall | C32×C23×C31 ⋊ C4 |
| Hall | C32×C31 ⋊ Dic23 |
| Hall | C32×C23 ⋊ Dic31 |
| Sylow | C31 ⋊ C32×Dic23 |
| Sylow | C23 ⋊ C32×Dic31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D713 |
| commutator, hypocenter | C23×C31 | C32×C4 |
| Frattini | C2 | C32×D713 |
| Fitting, socle, prime radical | C2×C32×C23×C31 | C2 |
| cosocle | C2×C23×C31 | C2×C32 |
| LCS | G ▷ C23×C31 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 25668 |
6444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(25668, 52);