Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×C4⋊C16 ⋊ C2 |
| Sylow | C61 ⋊ #2207 |
174 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|b^2=d,c^2=g,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^60,e^c=ef,f^c=fg,h^c=h^601229 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29593445, #29593446, #29593452, … |
| maximal normal subgroup of | #29593445, #29593446, #29593452, … |
| maximal quotient of | #29594137, #29594191, #29594310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6551);