Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C8 · Schur multiplier (H2) = C210×C3 |
| direct product | C24×C3⋊(C3⋊C8) |
| derived, Sylow | C32 ⋊ C24×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | C3⋊D3 |
| commutator, hypocenter | C32 | C24×C8 |
| Frattini | C4 | C24×C3⋊D3 |
| Fitting | C24×C32×C4 | C2 |
| socle, prime radical | C25×C32 | C4 |
| cosocle | C32×C4 | C25 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C24×C4 | |
5928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1152 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 152433);