Finite Group DatabasebetaFinite Group Databasebeta| order | 10816 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×D13⋊#261 |
| Fitting, socle | C23×C132 ⋊ C2×C4 |
| derived, Sylow | C132 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D13⋊#261 |
| commutator, hypocenter | C132 | C24×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C132 | C2×C4 |
| prime radical | C23×D132 | C2 |
| cosocle | C13⋊D13 | C25 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C23 | |
3432 conjugacy classes of subgroups; only the 831 normal subgroups are shown.
This group has 3432 conjugacy classes of subgroups — too many to draw. Only its 831 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 208 |
304 conjugacy classes. The character table is too large to display.
| maximal quotient of | #72259364 |
Past the SmallGroups library coverage — no SmallGroups id.