Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#10592440 |
| Fitting | C2×C32×#99 ⋊ C2 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
3054 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 3054 conjugacy classes of subgroups — too many to draw. Only its 313 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
120 conjugacy classes — view the full character table.
| maximal subgroup of | #72214782, #72214828, C2×C3⋊D3×B(4,𝔽2), … |
| maximal normal subgroup of | #72214782, #72214828, C2×C3⋊D3×B(4,𝔽2), … |
| maximal quotient of | #72214782 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99262);