Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27×C3 |
| direct product | C2×#10592943 |
| Fitting | C2×C32×H(5,𝔽2) ⋊ C2 |
| Sylow | C32 ⋊ C2×B(4,𝔽2) |
3054 conjugacy classes of subgroups; only the 393 normal subgroups are shown.
This group has 3054 conjugacy classes of subgroups — too many to draw. Only its 393 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | #72214760, #72214841, C2×C3⋊D3×B(4,𝔽2), … |
| maximal normal subgroup of | #72214760, #72214841, C2×C3⋊D3×B(4,𝔽2), … |
| maximal quotient of | #72214760 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 99259);