Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×C3×#393⋊C3 |
| unambiguous semidirect product | (C2×#393)⋊C32 |
| unambiguous semidirect product | (C2×C3×#393)⋊C3 |
| Fitting | C2×C3×#393 ⋊ C3 |
| derived | C22×Q8 ⋊ C22×C32 |
| Sylow | C2×#393 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #120⋊C3 |
| commutator, cosocle, hypocenter | C22×Q8 | C22×C32 |
| Frattini | C23 | C22×C3×A4 |
| Fitting | C2×C3×#393 | C3 |
| socle | C24×C3 | C2×A4 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C22×C3 | |
564 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C3×#35346⋊C3, C2×D3×#393⋊C3 |
| maximal normal subgroup of | C2×D3×#393⋊C3 |
| maximal quotient of | C2×C3×#2032⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153445);