Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #1940 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×#6923 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | C2×C4⋊C4×C61 | C4 |
| hypercenter | C2×C4⋊C4 | #6923 |
| hypocenter | C61 | #1940 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊C4 | |
248 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 92 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^2=f,c^2=e,f^2=g,b^a=bd,c^a=ce,h^a=h^50,c^b=cg,h^b=h^11,h^c=h^60,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | D61⋊#1940, C2×#21461921, #30616117, … |
| maximal normal subgroup of | D61⋊#1940, C2×#21461921, #30616117, … |
| maximal quotient of | #30601515, #30601518, #30601521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20612);