Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #131×C113 ⋊ C2 |
| Sylow | C113 ⋊ #578 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22×D452 |
| commutator | C4×C113 | C24 |
| Frattini | C4 | C23×D113 |
| Fitting | #131×C113 | C2 |
| socle | C2×C113 | C22×D4 |
| hypercenter | #131 | D113 |
| hypocenter | C113 | #578 |
| LCS | G ▷ C4×C113 ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C2 ◁ #41 ◁ #131 | |
248 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,g^a=g^112,e^b=ef,g^b=g^112,d^c=df1142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28392536, #28392540, #28392550, … |
| maximal normal subgroup of | #28392536, #28392540, #28392550, … |
| maximal quotient of | #28399108, #28399174, #28399419, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1366);