Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C61 ⋊ #1924 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22×C4 | C22×D61 |
| commutator, socle | C23×C61 | C22×C4 |
| Fitting | C4×C22⋊C4×C61 | C2 |
| hypercenter | C4×C22⋊C4 | D61 |
| hypocenter | C61 | #1924 |
| LCS | G ▷ C23×C61 ▷ C61 | |
| UCS | C1 ◁ C22×C4 ◁ C4×C22⋊C4 | |
280 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 105 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,b^2=df,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^60,c^b=cg,h^b=h^601244 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×#1924, C2×#21446434, #29682309, … |
| maximal normal subgroup of | D61×#1924, C2×#21446434, #29682309, … |
| maximal quotient of | #29578216, #29578223, #29578230, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 5125);