Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×D8×C113 ⋊ C2 |
| Sylow | C113 ⋊ #469 |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|b^2=df,d^2=f,b^a=bd,c^a=ce,d^a=df,c^b=cf,g^c=g^112800 conjugacy classes — view the full character table.
| maximal subgroup of | #28392518, #28392787, #469×D113, … |
| maximal normal subgroup of | #28392518, #28392787, #469×D113, … |
| maximal quotient of | #28390050, #28390055, #28390084, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 799);