Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C61 ⋊ #1422 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C4⋊#6923 |
| commutator | C4×C61 | C2×C16 |
| Frattini | C2×C8 | C2×#6923 |
| Fitting | C4×C8×C61 | C4 |
| socle | C2×C61 | C4⋊C16 |
| hypercenter | C4×C8 | #6923 |
| hypocenter | C61 | #1422 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ C4×C8 | |
58 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,b^2=c,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^11,h^d=h^60536 conjugacy classes — view the full character table.
| maximal subgroup of | #30594896, #30594897, #30594898, … |
| maximal normal subgroup of | #30594896, #30594897, #30594898, … |
| maximal quotient of | #30595056, #30595064, #30595086, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19669);