Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10591725 |
| Fitting | C25×C32 ⋊ C22 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #63983 |
| commutator, cosocle | C23×C32 | C24 |
| Frattini | C23 | C22×D32 |
| Fitting | C25×C32 | C22 |
| socle | C22×C32 | #120 |
| hypercenter | C25 | D32 |
| hypocenter | C32 | C2×B(4,𝔽2) |
| LCS | G ▷ C23×C32 ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22 ◁ C24 ◁ C25 | |
2367 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 2367 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#10591725, C2×#13166068, C2×#11865254, … |
| maximal normal subgroup of | C2×#11865254, #72252260, #72252270, … |
| maximal quotient of | D3×#10591725, #72252260, #72252324, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99270);