Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28×C3 |
| direct product | C2×#10592370 |
| Fitting | C2×C32×#95 ⋊ C2 |
| Sylow | C32 ⋊ C2×#392 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C3⋊D3 |
| commutator, cosocle | C23×C32 | C24 |
| Frattini | C23 | C23×C3⋊D3 |
| Fitting | C2×C32×#95 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C2×#95 | C3⋊D3 |
| hypocenter | C32 | C2×#392 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C2×#95 | |
5436 conjugacy classes of subgroups; only the 705 normal subgroups are shown.
This group has 5436 conjugacy classes of subgroups — too many to draw. Only its 705 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | #72214934, #72215029, C2×C3⋊D3×#392, … |
| maximal normal subgroup of | #72214934, #72215029, C2×C3⋊D3×#392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42099);