Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C61 ⋊ #2932 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×#6923 |
| commutator, socle | C22×C61 | C23×C4 |
| Fitting | #124×C61 | C4 |
| hypercenter | #124 | #6923 |
| hypocenter | C61 | #2932 |
| LCS | G ▷ C22×C61 ▷ C61 | |
| UCS | C1 ◁ C22 ◁ #124 | |
484 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 162 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=f,c^2=f,f^2=g,b^a=be,c^a=cg,d^a=dg,h^a=h^11,d^b=dg,h^c=h^11,h^d=h^60,h^f=h^60254 conjugacy classes — view the full character table.
| maximal subgroup of | #30606579, #30606584, #30616916, … |
| maximal normal subgroup of | #30606579, #30606584, #30616916, … |
| maximal quotient of | #30613015, #30613019, #30613023, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 21236);