Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210×C3 |
| direct product | D42×C3⋊D3 |
| Fitting | C32×D42 ⋊ C2 |
| Sylow | C32 ⋊ C2×D42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×C3⋊D3 |
| commutator, socle, cosocle | C22×C32 | C25 |
| Fitting | C32×D42 | C2 |
| hypercenter | D42 | C3⋊D3 |
| hypocenter | C32 | C2×D42 |
| LCS | G ▷ C22×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ D42 | |
7608 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
150 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D3×#3484, C3⋊D3×#3498, D4×C3⋊D3×S4, … |
| maximal normal subgroup of | C3⋊D3×#3484, C3⋊D3×#3498, #72258015, … |
| maximal quotient of | C3⋊D3×#2403, C3⋊D3×#2433 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 136319);