Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | D4×#15668449 |
| Fitting | C2×C4×D4×C181 ⋊ C2 |
| Sylow | C181 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D181 |
| commutator, socle, cosocle | C22×C181 | C25 |
| Frattini | C22 | C24×D181 |
| Fitting | C2×C4×D4×C181 | C2 |
| hypercenter | C2×C4×D4 | D181 |
| hypocenter | C181 | D4×#41 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 | |
1648 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
3650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 17998);