Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C215×C3 |
| direct product | C23×D4×C3⋊D3 |
| Fitting | C23×C32×D4 ⋊ C2 |
| Sylow | C32 ⋊ C24×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C3⋊D3 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C23×C32×D4 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C23×D4 | C3⋊D3 |
| hypocenter | C32 | C24×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
31656 conjugacy classes of subgroups; only the 5257 normal subgroups are shown.
This group has 31656 conjugacy classes of subgroups — too many to draw. Only its 5257 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3484, #72214219, C22×C3⋊D3×#120, … |
| maximal normal subgroup of | C3⋊D3×#3484, #72214219, C22×C3⋊D3×#120, … |
| maximal quotient of | C3⋊D3×#3484, C3⋊D3×#3498, C22×C3⋊D3×#120, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153167);