Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10591531 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
2367 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
108 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11865254, #72252272, #72252278, … |
| maximal normal subgroup of | C2×#11865254, #72252272, #72252278, … |
| maximal quotient of | #72252278, #72252345, #72252391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99271);