Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4 |
| direct product | C23×C4×Dic181 |
| derived, Sylow | C181 ⋊ C23×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | D181 |
| commutator, hypocenter | C181 | C23×C42 |
| Frattini | C22 | C24×D181 |
| Fitting | C24×C4×C181 | C2 |
| socle, prime radical | C25×C181 | C22 |
| cosocle | C22×C181 | C25 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C24×C4 | |
3000 conjugacy classes of subgroups.
| transitive degree | μt(G) = 23168 |
5888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 17665);