Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | #104×D113 |
| Fitting | #104×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#104 |
170 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
812 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#104×D113, #421×D113, #28399118, … |
| maximal normal subgroup of | C2×#104×D113, #421×D113, #28399118, … |
| maximal quotient of | D4⋊C8×D113, Q8⋊C8×D113, #28388953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 560);