Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C22⋊C4×C61 ⋊ C4 |
| Sylow | C61 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 94 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=f,c^2=e,b^a=bd,f^a=fg,h^a=h^60,d^b=dg,h^b=h^11,h^c=h^60,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #30594392, #30594651, #30597492, … |
| maximal normal subgroup of | #30594392, #30594651, #30597492, … |
| maximal quotient of | #30597446, #30597449, #30597456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20257);