Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C211×C3 |
| direct product | C22×#64162 |
| Fitting | C26×C32 ⋊ C2 |
| Sylow | C32 ⋊ C22×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×C3⋊D3 |
| commutator, cosocle | C22×C32 | C25 |
| Frattini | C22 | C24×C3⋊D3 |
| Fitting | C26×C32 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C26 | C3⋊D3 |
| hypocenter | C32 | C22×#120 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C24 ◁ C26 | |
13632 conjugacy classes of subgroups; only the 1801 normal subgroups are shown.
This group has 13632 conjugacy classes of subgroups — too many to draw. Only its 1801 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
312 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C3⋊D3×#120, #72215002, C22×#11722396, … |
| maximal normal subgroup of | C22×C3⋊D3×#120, #72215002, C22×C3×#64162 |
| maximal quotient of | C22×C3×#64162 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 134256);