Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×Q8×C113 ⋊ C4 |
| Sylow | C113 ⋊ #421 |
154 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 48 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,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^98,c^b=cf,d^b=df,g^b=g^112,g^c=g^112,g^e=g^112302 conjugacy classes — view the full character table.
| maximal subgroup of | #28406425, #28406426, #28406571, … |
| maximal normal subgroup of | #28406425, #28406426, #28406571, … |
| maximal quotient of | #28405872, #28405875, #28405876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1548);