Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#19153864 |
| Fitting | C23×Q8×C181 ⋊ C2 |
| Sylow | C181 ⋊ C22×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D181 |
| commutator, cosocle | C2×C181 | C26 |
| Frattini | C2 | C25×D181 |
| Fitting | C23×Q8×C181 | C2 |
| socle | C23×C181 | C24 |
| hypercenter | C23×Q8 | D181 |
| hypocenter | C181 | C22×2−1+4 |
| LCS | G ▷ C2×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
5872 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 5872 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11584 |
3668 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 19315);