Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #343 |
98 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=cf,g^a=g^112,d^b=df1142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28388577, #28388578, #28388580, … |
| maximal normal subgroup of | #28388577, #28388578, #28388580, … |
| maximal quotient of | #28388417, #28388424, #28388430, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 318);