Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C16×C113 ⋊ C2 |
| 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^112,c^b=ce,e^b=ef,g^b=g^1121814 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #359×D113, C2×#20298406, #28392300, … |
| maximal normal subgroup of | #359×D113, C2×#20298406, #28392300, … |
| maximal quotient of | #28388536, #28388539, #28388590, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 357);