Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×#3026⋊C3 |
| unambiguous semidirect product | #3026⋊C32 |
| unambiguous semidirect product | (C3×#3026)⋊C3 |
| Fitting | C3×#3026 ⋊ C3 |
| Sylow | #3026 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C2×#120⋊C3 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C22×C32 |
| Frattini | C23 | C22×C3×A4 |
| Fitting | C3×#3026 | C3 |
| hypercenter | C22×C3 | #120⋊C3 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C3 ◁ C22×C3 | |
416 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
69 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#72209831, D3×#3026⋊C3, C3×#11714170, … |
| maximal normal subgroup of | D3×#3026⋊C3, C3×#11714170, #72231666, … |
| maximal quotient of | C2×C3×#3026⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153601);