Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C32×#10624382 |
| Fitting | C32×C181 ⋊ C4 |
| derived, Sylow | C181 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | #10624382 |
| commutator, hypocenter | C181 | C4×C32 |
| Frattini | C16 | C2×#10624382 |
| Fitting | C32×C181 | C4 |
| socle | C2×C181 | C4×C16 |
| prime radical | C2×D181 | C2×C16 |
| cosocle | C16×D181 | C22 |
| LCS | G ▷ C181 | |
| UCS | C1 ◁ C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5792 |
1568 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19613);