Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210 |
| direct product | C23×C8×D181 |
| Fitting | C23×C8×C181 ⋊ C2 |
| derived, Sylow | C181 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D181 |
| commutator, hypocenter | C181 | C24×C8 |
| Frattini | C4 | C24×D181 |
| Fitting | C23×C8×C181 | C2 |
| socle | C24×C181 | C2×C4 |
| prime radical | C24×D181 | C4 |
| cosocle | C4×C181 | C25 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C23×C8 | |
1976 conjugacy classes of subgroups.
| transitive degree | μt(G) = 11584 |
5888 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19208);