Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×#4741 |
| Fitting | C32×#99 ⋊ C22 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D3×#882 |
| commutator, cosocle | C23×C32 | C24 |
| Frattini | C23 | C22×D32 |
| Fitting | C32×#99 | C22 |
| socle | C2×C32 | C2×#120 |
| hypercenter | #99 | D32 |
| hypocenter | C32 | C2×B(4,𝔽2) |
| LCS | G ▷ C23×C32 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C2 ◁ C23 ◁ #99 | |
2135 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
81 conjugacy classes — view the full character table.
| maximal subgroup of | D32×B(4,𝔽2), #72252984, #72253278, … |
| maximal normal subgroup of | D32×B(4,𝔽2) |
| maximal quotient of | #72252984, D3×#10591531, #72258286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99266);