Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #2327 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D61 |
| commutator | C22×C61 | C23×C4 |
| Fitting | C2×C4⋊Q8×C61 | C2 |
| socle | C23×C61 | C24 |
| hypercenter | C2×C4⋊Q8 | D61 |
| hypocenter | C61 | #2327 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C23 ◁ C2×C4⋊Q8 | |
516 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 237 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=g,b^2=g,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^60,c^b=ce,h^b=h^60884 conjugacy classes — view the full character table.
| maximal subgroup of | #29576717, #29576721, #29576745, … |
| maximal normal subgroup of | #29576717, #29576721, #29576745, … |
| maximal quotient of | #29601273, #29601325, #29601373, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 7230);