Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C23 |
| direct product | D3×#5935 |
| Fitting | C3×H(5,𝔽2) ⋊ C2×D3 |
| derived | C3×#997 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×#1020 |
| commutator, cosocle, hypocenter | C3×#997 | C22 |
| Fitting | C3×H(5,𝔽2) | C2×D3 |
| socle | C2×C3 | C2×#1020 |
| LCS | G ▷ C3×#997 | |
| UCS | C1 ◁ C2 | |
684 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 24 |
39 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D3×#5935, D3×#87520, #72215489, … |
| maximal normal subgroup of | C2×D3×#5935, D3×#87520, #72215489, … |
| maximal quotient of | C2×D3×#5935, D9×#5935, C3×D3×#5935, … |
| holomorph of | C3×Q8 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157665);