Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #100×C113 ⋊ C2 |
| Sylow | C113 ⋊ #455 |
152 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^112,d^b=df,e^b=ef,g^b=g^112,d^c=df632 conjugacy classes — view the full character table.
| maximal subgroup of | #28392565, #28392566, #28392576, … |
| maximal normal subgroup of | #28392565, #28392566, #28392576, … |
| maximal quotient of | #28389528, #28389533, #28389556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 729);