Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#69855 |
| Fitting | C32×C4×M16 ⋊ C2 |
| Sylow | C32 ⋊ #1490 |
703 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | #72219770, C3×#10771251, #72219778 |
| maximal normal subgroup of | #72219770, C3×#10771251, #72219778 |
| maximal quotient of | C3×#10705268 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 8692);