Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C2×D32×C4⋊C4 |
| Fitting | C2×C32×C4⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C23×C4⋊C4 |
5185 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C4×D32×D4, C2×D32×#106 |
| maximal normal subgroup of | C2×C4×D32×D4, C2×D32×#106 |
| maximal quotient of | #72222674, #72222860, C2×D32×#106 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 133839);