Finite Group DatabasebetaFinite Group Databasebeta| order | 23168 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | #395×D181 |
| Fitting | #395×C181 ⋊ C2 |
| Sylow | C181 ⋊ C2×#395 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D181 |
| commutator, socle, cosocle | C23×C181 | C24 |
| Fitting | #395×C181 | C2 |
| prime radical | C23×D181 | C23 |
| hypercenter | #395 | D181 |
| hypocenter | C181 | C2×#395 |
| LCS | G ▷ C23×C181 ▷ C181 | |
| UCS | C1 ◁ C23 ◁ #395 | |
908 conjugacy classes of subgroups; only the 223 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 223 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 11584 |
2024 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23168, 7718);