Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C61 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C32 | #6923 |
| commutator, hypocenter | C61 | C128 |
| Fitting | C32×C61 | C4 |
| socle | C2×C61 | C64 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C32 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^11,h^b=h^60608 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460634, D61⋊C128, #30595317, … |
| maximal normal subgroup of | C2×#21460634, D61⋊C128, #30595317, … |
| maximal quotient of | #30593918, C2×#21460634 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19325);