Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×Q8×C61 ⋊ C2 |
| Sylow | C61 ⋊ #3380 |
352 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 133 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,b^2=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^60,d^b=de,f^c=fg,h^c=h^601235 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29593708, #29593712, #29593736, … |
| maximal normal subgroup of | #29593708, #29593712, #29593736, … |
| maximal quotient of | #29696611, C4⋊C4×D488, #29698427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17378);