Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#11715840 |
| Fitting | C2×2−1+6 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | C22×#1020 |
| commutator, cosocle, hypocenter | #997 | C24 |
| Frattini | C2 | C23×#1020 |
| Fitting | C2×2−1+6 | D3 |
| hypercenter | C2×Q8 | #1020 |
| LCS | G ▷ #997 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
12496 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 12496 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
86 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72233470, C2×#72236876, C2×#72236908, … |
| maximal normal subgroup of | C2×#72233470, C2×#72236876, C2×#72236908, … |
Past the SmallGroups library coverage — no SmallGroups id.