Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#16813608 |
| Fitting | C2×C22⋊C4×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#124 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D113 |
| commutator | C22×C113 | C24 |
| Frattini | C22 | C23×D113 |
| Fitting | C2×C22⋊C4×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C2×C22⋊C4 | D113 |
| hypocenter | C113 | C2×#124 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
330 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 119 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388924, C4×#16813608, #28393115, … |
| maximal normal subgroup of | #28388924, C4×#16813608, #28393115, … |
| maximal quotient of | C2×#20298462, C2×#20298486, C2×#20298487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1064);