Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C3 · Schur multiplier (H2) = C29 |
| direct product | C3×#87277 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ #3585 |
3377 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
225 conjugacy classes — view the full character table.
| maximal subgroup of | #72214349, C3×#10826599, C3×#10826481, … |
| maximal normal subgroup of | #72214349, C3×#10826599, C3×#10826481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153045);