Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C61 ⋊ #2883 |
800 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 289 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=f,b^a=be,e^a=eg,h^a=h^60,f^b=fg,d^c=dg1061 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29597598, #29597602, #29597612, … |
| maximal normal subgroup of | #29597598, #29597602, #29597612, … |
| maximal quotient of | #29645832, #29645838, #29645920, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 12971);