Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10590410 |
| Fitting | C2×C32×C22⋊C4 ⋊ C22 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
2367 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 2367 conjugacy classes of subgroups — too many to draw. Only its 212 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11865254, #72252259, #72252272, … |
| maximal normal subgroup of | C2×#11865254, #72252259, #72252272, … |
| maximal quotient of | #72252259, #72252306, #72252337, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99274);