Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C61 ⋊ #3383 |
324 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 324 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=eg,b^2=eg,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^c=h^60785 conjugacy classes — view the full character table.
| maximal subgroup of | #29670178, #29670181, #29670186, … |
| maximal normal subgroup of | #29670178, #29670181, #29670186, … |
| maximal quotient of | #29696623, #29696627, C4⋊C4×#11758202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17397);