Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C61 ⋊ #2169 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×#6923 |
| commutator, socle | C22×C61 | C22×C8 |
| Fitting | C4×D4×C61 | C4 |
| hypercenter | C4×D4 | #6923 |
| hypocenter | C61 | #2169 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
162 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 74 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,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^11,c^b=cg,h^c=h^11,h^e=h^60356 conjugacy classes — view the full character table.
| maximal subgroup of | #30605878, #30605879, #30605882, … |
| maximal normal subgroup of | #30605878, #30605879, #30605882, … |
| maximal quotient of | #30605882, #30605923, #30605934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 20894);