Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×D9×H(5,𝔽2) |
| Fitting | C2×C9×H(5,𝔽2) ⋊ C2 |
| Sylow | C9 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D9 |
| commutator, cosocle | C2×C9 | C26 |
| Frattini | C2×C3 | C25×D3 |
| Fitting | C2×C9×H(5,𝔽2) | C2 |
| socle | C22×C3 | C24×D3 |
| hypercenter | C2×H(5,𝔽2) | D9 |
| hypocenter | C9 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
9840 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | D9×#3498, D9×#3484, C2×D9×#453, … |
| maximal normal subgroup of | D9×#3498, D9×#3484, C2×D9×#453, … |
| maximal quotient of | D9×#3498, D9×#3484, C2×#13164733, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153219);