Finite Group DatabasebetaFinite Group Databasebeta| order | 7232 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C113 ⋊ #504 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×#90673 |
| commutator, socle | C2×C113 | C22×C8 |
| Fitting | #41×C113 | C4 |
| hypercenter | #41 | #90673 |
| hypocenter | C113 | #504 |
| LCS | G ▷ C2×C113 ▷ C113 | |
| UCS | C1 ◁ C4 ◁ #41 | |
84 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,113|a^2=d,d^2=e,e^2=f,g^a=g^98,c^b=cf,g^d=g^112320 conjugacy classes — view the full character table.
| maximal subgroup of | #28406961, #28406962, #28406964, … |
| maximal normal subgroup of | #28406961, #28406962, #28406964, … |
| maximal quotient of | #28406783, #28406804, #28406909, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7232, 1607);