Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C113 ⋊ #497 |
124 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=f,b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^112,c^b=cf,g^b=g^112800 conjugacy classes — view the full character table.
| maximal subgroup of | #28388733, #28388735, #28389880, … |
| maximal normal subgroup of | #28388733, #28388735, #28389880, … |
| maximal quotient of | #28390195, #28390209, #28390222, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 944);