Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| direct product | C2×A4⋊(#41⋊C3) |
| unambiguous semidirect product | (C2×A4)⋊(#41⋊C3) |
| unambiguous semidirect product | (C2×#5919)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | A4×S4 |
| commutator, cosocle, hypocenter | Q8×A4 | C22×C3 |
| Frattini | C2 | C2×A4×S4 |
| Fitting | C23×Q8 | C3×D3 |
| socle | C24 | D3×A4 |
| LCS | G ▷ Q8×A4 | |
| UCS | C1 ◁ C22 | |
459 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 459 conjugacy classes of subgroups — too many to draw. Only its 36 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157487);