Finite Group DatabasebetaFinite Group Databasebeta| order | 8112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D4×#11759817 |
| Fitting | D4×C132 ⋊ C2×C3 |
| Hall | D4×C13×D13 ⋊ C3 |
| Hall | #92788 ⋊ C2×D4 |
| Sylow | C132 ⋊ C2×C3×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11759817 |
| commutator, socle, cosocle | C2×C132 | C23×C3 |
| Fitting | D4×C132 | C2×C3 |
| hypercenter | D4 | #11759817 |
| hypocenter | C132 | C2×C3×D4 |
| LCS | G ▷ C2×C132 ▷ C132 | |
| UCS | C1 ◁ C2 ◁ D4 | |
312 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 104 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | D4×#11759815⋊C2, #72259622, #72259641 |
| maximal normal subgroup of | D4×#11759815⋊C2, #72259622, #72259641 |
Past the SmallGroups library coverage — no SmallGroups id.