Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | Q82×C61 ⋊ C2 |
| Sylow | C61 ⋊ #3385 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×C22⋊D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | Q82×C61 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | Q82 | D61 |
| hypocenter | C61 | #3385 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 ◁ Q82 | |
340 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 133 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=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,c^b=cg,d^b=de,f^c=fg,h^c=h^60779 conjugacy classes — view the full character table.
| maximal subgroup of | #29669511, #29669513, #29669556, … |
| maximal normal subgroup of | #29669511, #29669513, #29669556, … |
| maximal quotient of | #29696634, #29696671, #29698303, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17416);