Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C22⋊C8×C61 ⋊ C2 |
| Sylow | C61 ⋊ #1516 |
284 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 73 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,d^2=g,b^a=bd,c^a=cg,d^a=df,h^a=h^60,c^b=cf,d^b=dg,e^b=efg,h^b=h^601232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29572186, #29572187, #29572190, … |
| maximal normal subgroup of | #29572186, #29572187, #29572190, … |
| maximal quotient of | #29568023, #29568028, #29568043, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 3067);