Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×D3×C3⋊C16 |
| derived, Sylow | C32 ⋊ C2×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C8 | D32 |
| commutator, hypocenter | C32 | C2×C4×C16 |
| Frattini | C2×C8 | C2×D32 |
| Fitting | C32×C4×C8 | C22 |
| socle | C22×C32 | C22×C8 |
| prime radical | C22×C3×D3 | C2×C8 |
| cosocle | C2×C32×C8 | C23 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C4×C8 | |
461 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, 29825);