Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×#10593558 |
| Fitting | C2×C32×D4 ⋊ Q8 |
| Sylow | C32 ⋊ C2×#474 |
598 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
48 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D8×PSU(3,𝔽2) |
| maximal normal subgroup of | C2×D8×PSU(3,𝔽2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 102279);