Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | C3⋊D3×#394 |
| Fitting | C32×#394 ⋊ C2 |
| Sylow | C32 ⋊ C2×#394 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×C3⋊D3 |
| commutator, socle, cosocle | C23×C32 | C24 |
| Fitting | C32×#394 | C2 |
| prime radical | C22×D4×C3⋊D3 | C2 |
| hypercenter | #394 | C3⋊D3 |
| hypocenter | C32 | C2×#394 |
| LCS | G ▷ C23×C32 ▷ C32 | |
| UCS | C1 ◁ C23 ◁ #394 | |
3756 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
132 conjugacy classes — view the full character table.
| maximal quotient of | C3⋊D3×#1438 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 42142);