Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×#15668448 |
| Fitting | C23×D4×C181 ⋊ C2 |
| Sylow | C181 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D181 |
| commutator, cosocle | C2×C181 | C26 |
| Frattini | C2 | C25×D181 |
| Fitting | C23×D4×C181 | C2 |
| socle | C24×C181 | C23 |
| hypercenter | C23×D4 | D181 |
| hypocenter | C181 | C23×#41 |
| LCS | G ▷ C2×C181 ▷ C181 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
6520 conjugacy classes of subgroups; only the 3301 normal subgroups are shown.
This group has 6520 conjugacy classes of subgroups — too many to draw. Only its 3301 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11584 |
3680 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19307);