Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#340 ⋊ C2 |
| Sylow | C61 ⋊ #2034 |
| 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 | #2034 |
| LCS | G ▷ C22×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,61|c^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^60,c^b=cf,h^b=h^60,e^c=eg,h^c=h^60872 conjugacy classes — view the full character table.
| maximal subgroup of | D61×#2034, C2×#21447011, #29707497, … |
| maximal normal subgroup of | D61×#2034, C2×#21447011, #29707497, … |
| maximal quotient of | #29583291, #29583298, #29583381, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5702);