Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D8×#157 |
| Fitting | C2×C32×D8 ⋊ C4 |
| Sylow | C32 ⋊ C2×C4×D8 |
954 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
84 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, 93835);