Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×D4×C113 ⋊ C2 |
| Sylow | C113 ⋊ #459 |
140 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|b^2=d,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^112,e^c=ef1139 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28389628, #28389630, #28389639, … |
| maximal normal subgroup of | #28389628, #28389630, #28389639, … |
| maximal quotient of | #28389915, #28389929, #28389939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 744);