Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C42×C113 ⋊ C4 |
| Sylow | C113 ⋊ #384 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator, socle | C22×C113 | C22×C4 |
| Fitting | C42×C113 | C4 |
| hypercenter | C42 | #90673 |
| hypocenter | C113 | #384 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C42 | |
186 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=d,c^2=e,b^a=bd,c^a=ce,g^a=g^98,g^f=g^112476 conjugacy classes — view the full character table.
| maximal subgroup of | #28405453, #28406442, #28406443, … |
| maximal normal subgroup of | #28405453, #28406442, #28406443, … |
| maximal quotient of | #28405752, #28405762, #28406506, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1495);