Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C61×#525 ⋊ C2 |
| Sylow | C61 ⋊ D4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D61 |
| commutator, socle | C22×C61 | C25 |
| Frattini | C22 | C24×D61 |
| Fitting | C61×#525 | C2 |
| hypercenter | #525 | D61 |
| hypocenter | C61 | D4×#41 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
1648 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|e^2=f,b^a=bf,c^a=cg,d^b=df,h^d=h^60890 conjugacy classes — view the full character table.
| maximal subgroup of | #29695682, #29695685, #29695693, … |
| maximal normal subgroup of | #29695682, #29695685, #29695693, … |
| maximal quotient of | #29839211, #29839214, #29839327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17993);