Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | D3×C3⋊C64 |
| unambiguous semidirect product | (C3×D3)⋊C64 |
| derived, Sylow | C32 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | D32 |
| commutator, hypocenter | C32 | C2×C64 |
| Fitting, cosocle | C32×C32 | C22 |
| socle | C2×C32 | C2×C32 |
| prime radical | C2×C3×D3 | C32 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C32 | |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
288 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 7101);