Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C22×C3×C22⋊SL(2,𝔽3) |
| Fitting | C24×C3×Q8 ⋊ C3 |
| derived | C22×Q8 ⋊ C22×C32 |
| Sylow | C24×Q8 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C3 | C22⋊A4 |
| commutator, cosocle, hypocenter | C22×Q8 | C22×C32 |
| Frattini | C2 | C22×C3×C22⋊A4 |
| Fitting | C24×C3×Q8 | C3 |
| socle | C25×C3 | A4 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C23×C3 | |
2392 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 2392 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153903);