Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C61×#498 ⋊ C2 |
| Sylow | C61 ⋊ #3381 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D61 |
| commutator | C2×C4×C61 | C24 |
| Frattini | C2×C4 | C23×D61 |
| Fitting | C61×#498 | C2 |
| socle | C22×C61 | C22×D4 |
| hypercenter | #498 | D61 |
| hypocenter | C61 | #3381 |
| LCS | G ▷ C2×C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #498 | |
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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=eg,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^60,d^b=de,h^b=h^60,f^c=fg,h^c=h^60695 conjugacy classes — view the full character table.
| maximal subgroup of | #29669884, #29669891, #29669989, … |
| maximal normal subgroup of | #29669884, #29669891, #29669989, … |
| maximal quotient of | #29696614, #29696632, #29698413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 17390);