Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C27×C3 |
| direct product | C22×C3×D4×A4 |
| unambiguous semidirect product | C4⋊(C23×C3×A4) |
| Fitting | C24×C3×D4 ⋊ C3 |
| Sylow | C24×D4 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C3 | C22×A4 |
| commutator, cosocle | C23 | C24×C32 |
| Frattini | C2 | C24×C3×A4 |
| Fitting | C24×C3×D4 | C3 |
| socle | C25×C3 | C22×C3 |
| hypercenter | C22×C3×D4 | A4 |
| hypocenter | C22 | C22×C32×D4 |
| LCS | G ▷ C23 ▷ C22 | |
| UCS | C1 ◁ C23×C3 ◁ C22×C3×D4 | |
4776 conjugacy classes of subgroups; only the 624 normal subgroups are shown.
This group has 4776 conjugacy classes of subgroups — too many to draw. Only its 624 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
240 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D4×A42 |
| maximal normal subgroup of | C3×D4×A42 |
| maximal quotient of | C22×D4×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153873);