Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#16813629 |
| Sylow | C113 ⋊ C2×#131 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D113 |
| commutator | C2×C113 | C23×C4 |
| Frattini | C4 | C23×D113 |
| Fitting | C2×#41×C113 | C2 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C2×#41 | D113 |
| hypocenter | C113 | C2×#131 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
266 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390376, #28390377, #28390412, … |
| maximal normal subgroup of | #28390376, #28390377, #28390412, … |
| maximal quotient of | C2×#20298554, C4×#16813629, C2×#20298565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1312);