Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C4⋊(#120⋊C3) |
| unambiguous semidirect product | C4⋊(C3×#120⋊C3) |
| unambiguous semidirect product | #2847⋊C32 |
| unambiguous semidirect product | (C3×#2847)⋊C3 |
| Fitting | C3×#2847 ⋊ C3 |
| Sylow | #2847 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3 | C2×#120⋊C3 |
| commutator, cosocle | C25 | C22×C32 |
| Frattini | C23 | C22×C3×A4 |
| Fitting | C3×#2847 | C3 |
| socle | C23×C3 | C22×A4 |
| hypercenter | C3×C4 | #120⋊C3 |
| hypocenter | C24 | C32×D4 |
| LCS | G ▷ C25 ▷ C24 | |
| UCS | C1 ◁ C2×C3 ◁ C3×C4 | |
568 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153511);