Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| isoclinism | isoclinic class of #634 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214×C3 |
| direct product | C23×#3828 |
| Fitting | C24×C32×C4 ⋊ C2 |
| Sylow | C32 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×C3⋊D3 |
| commutator, cosocle | C2×C32 | C26 |
| Frattini | C2 | C25×C3⋊D3 |
| Fitting | C24×C32×C4 | C2 |
| socle | C24×C32 | C23 |
| hypercenter | C24×C4 | C3⋊D3 |
| hypocenter | C32 | C23×#41 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C4 | |
19560 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, 153201);