Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #359 |
56 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,c^2=ef,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^98,c^b=ce,e^b=ef,g^b=g^112,g^d=g^112218 conjugacy classes — view the full character table.
| maximal subgroup of | D113⋊#359, C2×#20299513, #28406888, … |
| maximal normal subgroup of | D113⋊#359, C2×#20299513, #28406888, … |
| maximal quotient of | #28405529, #28405530, #28405565, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1464);