Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×M16×C61 ⋊ C2 |
| Sylow | C61 ⋊ #1484 |
262 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 77 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=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^60,c^b=cfg,d^b=df,h^b=h^601238 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29571865, #29571868, #29571879, … |
| maximal normal subgroup of | #29571865, #29571868, #29571879, … |
| maximal quotient of | #29568438, #29568462, #29568479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2928);