Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C61 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | #6923 |
| commutator, hypocenter | C61 | C4×C32 |
| Frattini | C2×C8 | C2×#6923 |
| Fitting | C2×C16×C61 | C4 |
| socle | C22×C61 | C2×C16 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C2×C16 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,h^a=h^11,h^b=h^60,h^c=h^60608 conjugacy classes — view the full character table.
| maximal subgroup of | C32×#92420, #30594777, #92420⋊C32, … |
| maximal normal subgroup of | C32×#92420, #30594777, #92420⋊C32, … |
| maximal quotient of | #30594776, #30594786, #30595081, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19615);