Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | 2−1+4×D113 |
| Fitting | 2−1+4×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D113 |
| commutator, socle | C2×C113 | C25 |
| Fitting | 2−1+4×C113 | C2 |
| hypercenter | 2−1+4 | D113 |
| hypocenter | C113 | C2×2−1+4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ 2−1+4 | |
794 conjugacy classes of subgroups.
986 conjugacy classes — view the full character table.
| maximal subgroup of | #454×D113, #456×D113, #28399935, … |
| maximal normal subgroup of | #454×D113, #456×D113, #28399935, … |
| maximal quotient of | #519×D113, #520×D113, #28403783, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1381);