Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22⋊C8×C113 ⋊ C2 |
| Sylow | C113 ⋊ #480 |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|c^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^112,e^c=ef,g^c=g^1121139 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389561, #28389562, #28389573, … |
| maximal normal subgroup of | #28389561, #28389562, #28389573, … |
| maximal quotient of | #28390661, #28390764, #28390889, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 863);