Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2085 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D61 |
| commutator | C22×C4×C61 | C23 |
| Frattini | C22×C4 | C22×D61 |
| Fitting | C61×#340 | C2 |
| socle | C23×C61 | C2×D4 |
| hypercenter | #340 | D61 |
| hypocenter | C61 | #2085 |
| LCS | G ▷ C22×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
214 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 83 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=d,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^60,c^b=cf,f^b=fg,h^b=h^60,f^c=fg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2085, C2×#21447306, #29708991, … |
| maximal normal subgroup of | D61×#2085, C2×#21447306, #29708991, … |
| maximal quotient of | #29584959, #29584966, #29584973, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5997);