Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2150 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C22×C8 |
| Fitting | C22×C8×C61 | C4 |
| hypercenter | C22×C8 | #6923 |
| hypocenter | C61 | #2150 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C8 | |
172 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=d,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^11,h^b=h^60,h^e=h^60536 conjugacy classes — view the full character table.
| maximal subgroup of | #30594422, #30594426, #30594634, … |
| maximal normal subgroup of | #30594422, #30594426, #30594634, … |
| maximal quotient of | #30605746, #30605772, #30605801, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20844);