Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#10591522 |
| Fitting | C22×C32×D4 ⋊ C22 |
| Sylow | C32 ⋊ C2×#453 |
1937 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1937 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×#11864777, #72214366, #72214920, … |
| maximal normal subgroup of | C2×#11864777, #72214366, #72214920, … |
| maximal quotient of | #72219787, D3×#10591522, D7×#10591522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 98794);