Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C26 |
| direct product | C2×#11715717 |
| Fitting | C22×#585 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23 | C2×#1020 |
| commutator, cosocle | C2×#997 | C23 |
| Frattini | C22 | C22×#1020 |
| Fitting | C22×#585 | D3 |
| hypercenter | C22×C4 | #1020 |
| hypocenter | #997 | C2×D4 |
| LCS | G ▷ C2×#997 ▷ #997 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
8170 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 8170 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
74 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72245747, C2×#72245678, C2×#72245714, … |
| maximal normal subgroup of | C2×#72245747, C2×#72245678, C2×#72245714, … |
Past the SmallGroups library coverage — no SmallGroups id.