Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Q8⋊#11744762 |
| Fitting | Q8×C113 ⋊ C8 |
| Sylow | C113 ⋊ Q8⋊C8 |
70 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,b^2=e,c^2=e,d^2=f,b^a=bc,c^a=ce,g^a=g^18,c^b=ce,g^d=g^98,g^f=g^11298 conjugacy classes — view the full character table.
| maximal subgroup of | C2×Q8⋊#11744762, #28407692, #28407693, … |
| maximal normal subgroup of | C2×Q8⋊#11744762, #28407692, #28407693, … |
| maximal quotient of | #28407574, #28407575, #28407582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1637);