Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×D4×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1505 |
272 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 58 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=e,c^2=f,d^2=g,b^a=bd,d^a=df,h^a=h^11,c^b=cf,d^b=dg,e^b=efg,h^c=h^60,h^e=h^60332 conjugacy classes — view the full character table.
| maximal subgroup of | #30598637, #30598638, #30598641, … |
| maximal normal subgroup of | #30598637, #30598638, #30598641, … |
| maximal quotient of | #30595401, #30595403, #30595429, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19900);