Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #435 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator, socle | C22×C113 | C22×C4 |
| Fitting | C4⋊C4×C113 | C4 |
| hypercenter | C4⋊C4 | #90673 |
| hypocenter | C113 | #435 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
124 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 46 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,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^98,g^b=g^112,g^c=g^98,g^e=g^112308 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20299628, D113⋊#435, #28407290, … |
| maximal normal subgroup of | C2×#20299628, D113⋊#435, #28407290, … |
| maximal quotient of | #28406174, #28406178, #28406182, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1579);