Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C3 · Schur multiplier (H2) = C214 |
| direct product | C3×#87568 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ H(7,𝔽2) |
12433 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×#11923832 |
| maximal normal subgroup of | C3×#11923832 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 153287);