Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C113 ⋊ #361 |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,c^2=e,d^2=f,e^2=f,b^a=bc,c^a=ce,e^a=ef,g^a=g^98,c^b=cef,d^b=df,e^b=ef,g^d=g^112212 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299516, D113⋊#361, #28406901, … |
| maximal normal subgroup of | C2×#20299516, D113⋊#361, #28406901, … |
| maximal quotient of | #28405532, #28405533, #28405564, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1467);