Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C61 ⋊ #1778 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×C4⋊#6923 |
| commutator | C4×C61 | C2×C42 |
| Frattini | C2×C4 | C22×#6923 |
| Fitting | #97×C61 | C4 |
| socle | C22×C61 | C2×C4⋊C4 |
| hypercenter | #97 | #6923 |
| hypocenter | C61 | #1778 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
220 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 92 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=e,b^2=f,c^2=de,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=cg,d^b=dg,e^b=eg,h^b=h^11,h^f=h^60344 conjugacy classes — view the full character table.
| maximal subgroup of | #30606642, #30606768, C2×#21461639, … |
| maximal normal subgroup of | #30606642, #30606768, C2×#21461639, … |
| maximal quotient of | #30598015, #30598016, #30598019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20330);