Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×#90673 |
| Fitting | M16×C113 ⋊ C4 |
| Sylow | C113 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#90673 |
| commutator, socle | C2×C113 | C2×C42 |
| Fitting | M16×C113 | C4 |
| hypercenter | M16 | #90673 |
| hypocenter | C113 | C4×M16 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ M16 | |
142 conjugacy classes of subgroups.
320 conjugacy classes — view the full character table.
| maximal subgroup of | #100×#90673, #101×#90673, #104×#90673, … |
| maximal normal subgroup of | #100×#90673, #101×#90673, #104×#90673, … |
| maximal quotient of | M16×#11744753, #28405772, #28405775, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1509);