Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#41×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1796 |
536 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|a^2=f,b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^11,d^b=dg,h^b=h^60,f^c=fg,h^f=h^60329 conjugacy classes — view the full character table.
| maximal subgroup of | #30606876, #30606878, #30606884, … |
| maximal normal subgroup of | #30606876, #30606878, #30606884, … |
| maximal quotient of | #30598195, #30598196, #30598197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20363);