Finite Group DatabasebetaFinite Group Databasebeta| order | 16224 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C210 |
| direct product | C23×#11759815⋊C2 |
| Fitting, socle | C23×C132 ⋊ C22×C3 |
| derived, Sylow | C132 ⋊ C25×C3 |
| Hall | C23×D132 ⋊ C3 |
| Hall | #92788 ⋊ C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #11759815⋊C2 |
| commutator, cosocle, hypocenter | C132 | C25×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C132 | C22×C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C23 | |
3796 conjugacy classes of subgroups; only the 898 normal subgroups are shown.
This group has 3796 conjugacy classes of subgroups — too many to draw. Only its 898 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
256 conjugacy classes — view the full character table.
| maximal quotient of | #72259728 |
Past the SmallGroups library coverage — no SmallGroups id.