Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #117×C61 ⋊ C4 |
| Sylow | C61 ⋊ #2296 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Frattini | C22 | C23×#6923 |
| Fitting | #117×C61 | C4 |
| hypercenter | #117 | #6923 |
| hypocenter | C61 | #2296 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
656 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 218 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,d^2=f,b^a=be,c^a=cf,h^a=h^50,h^b=h^11,h^g=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | #30602861, #30602863, #30602880, … |
| maximal normal subgroup of | #30602861, #30602863, #30602880, … |
| maximal quotient of | #30608619, #30608626, C4×#16840709, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20970);