Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of Dic18 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C23×#3697 |
| Fitting | C24×C4×C9 ⋊ C2 |
| Sylow | C9 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D9 |
| commutator, cosocle | C2×C9 | C26 |
| Frattini | C2×C3 | C25×D3 |
| Fitting | C24×C4×C9 | C2 |
| socle | C24×C3 | C22×D3 |
| hypercenter | C24×C4 | D9 |
| hypocenter | C9 | C23×#41 |
| LCS | G ▷ C2×C9 ▷ C9 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C4 | |
9780 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
336 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153200);