Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | #97×D113 |
| Fitting | #97×C113 ⋊ C2 |
| Sylow | C113 ⋊ C2×#97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D113 |
| commutator | C2×C113 | C2×C42 |
| Fitting | #97×C113 | C2 |
| socle | C22×C113 | C22×C4 |
| hypercenter | #97 | D113 |
| hypocenter | C113 | C2×#97 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ #97 | |
146 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #329×D113, #330×D113, #28389159, … |
| maximal normal subgroup of | #329×D113, #330×D113, #28389159, … |
| maximal quotient of | #322×D113, #28388860, #28388862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 496);