Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C113 ⋊ C2×C22⋊C8 |
202 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,113|a^2=e,e^2=f,b^a=bd,g^a=g^98,g^c=g^112,g^e=g^112488 conjugacy classes — view the full character table.
| maximal subgroup of | #28405411, #28405416, #28405436, … |
| maximal normal subgroup of | #28405411, #28405416, #28405436, … |
| maximal quotient of | #28405800, #28405803, #28405806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1517);