Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2097 |
238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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=d,b^2=deg,c^2=g,d^2=g,e^2=g,b^a=bd,c^a=ce,c^b=cf,d^b=dg,e^b=eg,h^b=h^60,d^c=dg,e^c=eg,h^c=h^601232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#2097, C2×#21447366, #29709806, … |
| maximal normal subgroup of | D61×#2097, C2×#21447366, #29709806, … |
| maximal quotient of | #29585010, #29585039, #29585071, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6057);