Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#3585⋊C3 |
| unambiguous semidirect product | #3585⋊C32 |
| unambiguous semidirect product | (C3×#3585)⋊C3 |
| Fitting | C3×#3585 ⋊ C3 |
| Sylow | #3585 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C2×D4×A4 |
| commutator, cosocle | #41 | C23×C32 |
| Frattini | C4 | C23×C3×A4 |
| Fitting | C3×#3585 | C3 |
| hypercenter | C3×#137 | A4 |
| hypocenter | Q8 | C2×C32×D4 |
| LCS | G ▷ #41 ▷ Q8 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#137 | |
792 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
129 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#983⋊A4, C3×#11715001, D3×#3585⋊C3, … |
| maximal normal subgroup of | C3×#11715001, D3×#3585⋊C3, #72242452 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153817);