Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C113 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#90673 |
| commutator | C2×C113 | C22×C8 |
| Fitting | C4⋊C4×C113 | C4 |
| socle | C22×C113 | C22×C4 |
| hypercenter | C4⋊C4 | #90673 |
| hypocenter | C113 | C8×D4 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
134 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=e,c^2=e,e^2=f,b^a=bd,g^a=g^15,g^b=g^112,g^c=g^98,g^e=g^112320 conjugacy classes — view the full character table.
| maximal subgroup of | #28406154, #28406155, #28406158, … |
| maximal normal subgroup of | #28406154, #28406155, #28406158, … |
| maximal quotient of | #28406155, #28406159, #28406162, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1577);