Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×#11744751 |
| Sylow | C113 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D113 |
| commutator | C2×C113 | C22×C8 |
| Fitting | C4×Q8×C113 | C2 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C4×Q8 | D113 |
| hypocenter | C113 | C8×Q8 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
102 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389371, SD16×#11744751, #28389378, … |
| maximal normal subgroup of | #28389371, SD16×#11744751, #28389378, … |
| maximal quotient of | C4⋊C4×#11744751, #28391133, #28391293, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 675);