Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C22⋊C4×#90673 |
| Fitting | C22⋊C4×C113 ⋊ C4 |
| Sylow | C113 ⋊ C4×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator | C2×C113 | C2×C42 |
| Fitting | C22⋊C4×C113 | C4 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C22⋊C4 | #90673 |
| hypocenter | C113 | C4×C22⋊C4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C22⋊C4 | |
258 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
320 conjugacy classes — view the full character table.
| maximal subgroup of | #99×#90673, C2×C22⋊C4×#90673, #117×#90673, … |
| maximal normal subgroup of | #99×#90673, C2×C22⋊C4×#90673, #117×#90673, … |
| maximal quotient of | #95×#90673, #28405747, #28405749, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1487);