Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #501 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=d,c^2=e,e^2=f,b^a=bd,c^a=ce,e^a=ef,c^b=cf,g^b=g^112,g^c=g^112800 conjugacy classes — view the full character table.
| maximal subgroup of | #501×D113, C2×#20299006, #28401095, … |
| maximal normal subgroup of | #501×D113, C2×#20299006, #28401095, … |
| maximal quotient of | #28390741, #28391311, #28391313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 957);