Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| isoclinism | isoclinic class of D113 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C4×Dic113 |
| derived, Sylow | C113 ⋊ C22×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D113 |
| commutator, hypocenter | C113 | C22×C42 |
| Frattini | C22 | C23×D113 |
| Fitting | C23×C4×C113 | C2 |
| socle | C24×C113 | C22 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C23×C4 | |
498 conjugacy classes of subgroups.
1856 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #95×Dic113, C4×#16813529, #28388798, … |
| maximal normal subgroup of | #95×Dic113, C4×#16813529, #28388798, … |
| maximal quotient of | C2×C42×Dic113, C22×#16813529, C2×#20298444, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 994);