Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×Dic113 |
| Sylow | C113 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D113 |
| commutator | C2×C113 | C2×C42 |
| Fitting | C2×M16×C113 | C2 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C2×M16 | D113 |
| hypocenter | C113 | C4×M16 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
142 conjugacy classes of subgroups.
1160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390365, #100×Dic113, #28390369, … |
| maximal normal subgroup of | #28390365, #100×Dic113, #28390369, … |
| maximal quotient of | M16×#11744751, #28388855, #28388861, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 500);