Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #1417 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16840674 |
| commutator | C16×C61 | C2×C4 |
| Frattini | C16 | C2×#6923 |
| Fitting | Q32×C61 | C4 |
| socle | C2×C61 | #357 |
| hypercenter | Q32 | #6923 |
| hypocenter | C61 | #1417 |
| LCS | G ▷ C16×C61 ▷ C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ Q32 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,c^2=ef,d^2=g,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^11,c^b=ce,e^b=ef,f^b=fg,h^b=h^60,h^d=h^60203 conjugacy classes — view the full character table.
| maximal subgroup of | D61⋊#1417, C2×#21460971, #30608485, … |
| maximal normal subgroup of | D61⋊#1417, C2×#21460971, #30608485, … |
| maximal quotient of | #30594901, #30594902, #30594989, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19662);