Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #441 |
108 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,b^2=f,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,g^a=g^112,d^b=df,g^c=g^112806 conjugacy classes — view the full character table.
| maximal subgroup of | #28392466, #28392468, #441×D113, … |
| maximal normal subgroup of | #28392466, #28392468, #441×D113, … |
| maximal quotient of | #28389393, #28389446, #28389483, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 656);