Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2258 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C8 | C22×#6923 |
| commutator, socle | C2×C61 | C22×C16 |
| Fitting | M32×C61 | C4 |
| hypercenter | M32 | #6923 |
| hypocenter | C61 | #2258 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ M32 | |
106 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=d,d^2=e,e^2=f,f^2=g,h^a=h^11,c^b=cg,h^b=h^60,h^d=h^60380 conjugacy classes — view the full character table.
| maximal subgroup of | #30608559, #30608560, #30608562, … |
| maximal normal subgroup of | #30608559, #30608560, #30608562, … |
| maximal quotient of | #30608241, #30608242, #30608262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20934);