Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Sylow | C61 ⋊ #3461 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D61 |
| commutator, socle | C22×C61 | C25 |
| Fitting | C61×#537 | C2 |
| hypercenter | #537 | D61 |
| hypocenter | C61 | #3461 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #537 | |
1012 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|b^2=f,c^2=f,e^2=g,b^a=bf,c^a=cg,d^a=df,c^b=cf,h^c=h^60,h^e=h^60704 conjugacy classes — view the full character table.
| maximal subgroup of | #29652360, #29652366, #29652371, … |
| maximal normal subgroup of | #29652360, #29652366, #29652371, … |
| maximal quotient of | #29838705, #29838709, #29838969, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17938);