Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16813605 |
| Fitting | C23×C4×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#123 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D113 |
| commutator | C22×C113 | C24 |
| Frattini | C22 | C23×D113 |
| Fitting | C23×C4×C113 | C2 |
| socle | C23×C113 | C23 |
| hypercenter | C23×C4 | D113 |
| hypocenter | C113 | C2×#123 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C23 ◁ C23×C4 | |
342 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388920, #28388923, #28390984, … |
| maximal normal subgroup of | #28388920, #28388923, #28390984, … |
| maximal quotient of | C2×#20298461, C2×#20298471, C2×#20298477, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1052);