Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| direct product | A4×#939 |
| unambiguous semidirect product | (C22×#939)⋊C3 |
| Fitting | C23×C3×D4 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D3×A4 |
| commutator, socle, cosocle | C24×C3 | C23×C3 |
| Fitting | C23×C3×D4 | C2×C3 |
| hypercenter | C2×D4 | D3×A4 |
| hypocenter | C22×C3 | C3×#121 |
| LCS | G ▷ C24×C3 ▷ C22×C3 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
1210 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 157363);