Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #341 |
90 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,c^2=f,d^2=f,e^2=f,b^a=bc,c^a=cf,e^a=ef,g^b=g^1121148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #341×D113, C2×#20298362, #28390299, … |
| maximal normal subgroup of | #341×D113, C2×#20298362, #28390299, … |
| maximal quotient of | #28388408, #28388410, #28388412, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 313);