Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #324 |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=ce,d^b=de,g^b=g^1121142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #324×D113, C2×#20298323, #28388885, … |
| maximal normal subgroup of | #324×D113, C2×#20298323, #28388885, … |
| maximal quotient of | #28388396, #28388398, #28388416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 274);