Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×#11744762 |
| Fitting | Q8×C113 ⋊ C8 |
| Sylow | C113 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11744762 |
| commutator, socle | C2×C113 | C22×C8 |
| Fitting | Q8×C113 | C8 |
| hypercenter | Q8 | #11744762 |
| hypocenter | C113 | C8×Q8 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
102 conjugacy classes of subgroups.
110 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1664);