Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | A4×#994 |
| Fitting, Sylow | C22×H(5,𝔽2) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×A42 |
| commutator, cosocle, hypocenter | C22×Q8 | C22×C32 |
| Fitting | C22×H(5,𝔽2) | C32 |
| socle | C23 | C22×C3×A4 |
| hypercenter | Q8 | A42 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
659 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 659 conjugacy classes of subgroups — too many to draw. Only its 58 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
76 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157680);