Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×#11744753 |
| Sylow | C113 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator | C2×C113 | C22×C8 |
| Fitting | C2×Q8×C113 | C4 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C2×Q8 | #90673 |
| hypocenter | C113 | C8×Q8 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
102 conjugacy classes of subgroups.
320 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#11744753, #28406158, Q16×#11744753, … |
| maximal normal subgroup of | SD16×#11744753, #28406158, Q16×#11744753, … |
| maximal quotient of | C4⋊C4×#11744753, #28406627, #28406671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1597);