Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×#135×C61 ⋊ C2 |
| Sylow | C61 ⋊ #3284 |
494 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=g,b^2=g,c^2=g,e^2=g,b^a=be,c^a=cf,d^a=dg,e^a=eg,d^b=de,e^b=eg,h^c=h^60,e^d=eg875 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#3284, C2×#21457543, #30555302, … |
| maximal normal subgroup of | D61×#3284, C2×#21457543, #30555302, … |
| maximal quotient of | #29670796, #29670801, #29670811, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 16234);