Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C22×C8 |
| Fitting | C4⋊C8×C61 | C4 |
| hypercenter | C4⋊C8 | #6923 |
| hypocenter | C61 | #2183 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4⋊C8 | |
126 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^50,h^c=h^11,h^e=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | #30605916, #30605918, #30605924, … |
| maximal normal subgroup of | #30605916, #30605918, #30605924, … |
| maximal quotient of | #30606700, #30606706, #30607767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20926);