Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C61×#563 ⋊ C2 |
| Sylow | C61 ⋊ #3545 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×#563 | C2 |
| hypercenter | #563 | D61 |
| hypocenter | C61 | #3545 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #563 | |
1060 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|c^2=fg,d^2=f,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^60,c^b=cg,d^b=df,h^b=h^60,h^c=h^60,h^e=h^60608 conjugacy classes — view the full character table.
| maximal subgroup of | #29661810, #29661818, #29661849, … |
| maximal normal subgroup of | #29661810, #29661818, #29661849, … |
| maximal quotient of | #29842843, #29843136, #29843414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 18868);