Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C42 |
No aliases for this group.
| Fitting | C4×C8×C61 ⋊ C4 |
| Sylow | C61 ⋊ #1274 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×#6923 |
| commutator | C4×C61 | C4×C8 |
| Frattini | C42 | C2×#6923 |
| Fitting | C4×C8×C61 | C4 |
| socle | C22×C61 | #95 |
| hypercenter | C4×C8 | #6923 |
| hypocenter | C61 | #1274 |
| LCS | G ▷ C4×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 | |
168 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 56 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=d,b^2=e,c^2=f,d^2=g,b^a=bc,e^a=ef,d^b=df,h^b=h^11,h^e=h^60524 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21460642, #30596003, #30596006, … |
| maximal normal subgroup of | C2×#21460642, #30596003, #30596006, … |
| maximal quotient of | #30593919, #30593924, #30593926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 19333);