Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C61×#332 ⋊ C2 |
| Sylow | C61 ⋊ #1553 |
242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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=fg,d^2=g,e^2=fg,b^a=bd,c^a=cf,d^a=df,d^b=dg,e^b=efg,h^b=h^60,h^c=h^60602 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#1553, C2×#21444523, #29648402, … |
| maximal normal subgroup of | D61×#1553, C2×#21444523, #29648402, … |
| maximal quotient of | #29568034, #29568044, #29568152, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3214);