Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210×C3 |
| direct product | C24×#622 |
| derived, Sylow | C32 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | #157 |
| commutator, hypocenter | C32 | C24×C8 |
| Frattini | C2 | C24×#157 |
| Fitting, socle, prime radical | C25×C32 | C4 |
| cosocle | C3⋊Dic3 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C25 | |
3338 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152435);