Finite Group DatabasebetaFinite Group Databasebeta| order | 3072 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#72236805 |
| Fitting | C2×#60402 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22 | #11713201 |
| commutator, cosocle | #5950 | C24 |
| Frattini | C22×C4 | C23×S4 |
| Fitting | C2×#60402 | D3 |
| hypercenter | C2×Q8 | #1020⋊C2 |
| hypocenter | #997 | C22×D4 |
| LCS | G ▷ #5950 ▷ #997 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
8836 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 8836 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 64 |
82 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72237002, C2×#72240982, C2×#72240984 |
| maximal normal subgroup of | C2×#72237002, C2×#72240982, C2×#72240984 |
Past the SmallGroups library coverage — no SmallGroups id.