Finite Group DatabasebetaFinite Group Databasebeta| order | 1536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#11713215 |
| Fitting | C22×#379 ⋊ D3 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#1020⋊C2 |
| commutator, cosocle | C2×C22⋊A4 | C24 |
| Frattini | C23 | C23×S4 |
| Fitting | C22×#379 | D3 |
| socle | C24 | C22×S4 |
| hypercenter | C23 | #1020⋊C2 |
| hypocenter | C22⋊A4 | C2×#41 |
| LCS | G ▷ C2×C22⋊A4 ▷ C22⋊A4 | |
| UCS | C1 ◁ C22 ◁ C23 | |
6692 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 6692 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#72220364, C2×#72220614, C2×#72220624 |
| maximal normal subgroup of | C2×#72220364, C2×#72220614, C2×#72220624 |
| maximal quotient of | C2×#72245467 |
Past the SmallGroups library coverage — no SmallGroups id.