Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#41×C113 ⋊ C2 |
| Sylow | C113 ⋊ #575 |
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,113|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,e^b=ef,g^b=g^1121142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28390933, #28390934, #28390936, … |
| maximal normal subgroup of | #28390933, #28390934, #28390936, … |
| maximal quotient of | #28399091, #28399093, #28399163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1347);