Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C61×#364 ⋊ C2 |
| Sylow | C61 ⋊ #2153 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D61 |
| commutator | C4×C61 | C22×C8 |
| Frattini | C2×C8 | C22×D61 |
| Fitting | C61×#364 | C2 |
| socle | C2×C61 | C2×C4⋊C8 |
| hypercenter | #364 | D61 |
| hypocenter | C61 | #2153 |
| LCS | G ▷ C4×C61 ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #364 | |
152 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 75 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=d,d^2=g,e^2=f,f^2=g,b^a=bd,d^a=dg,c^b=cg,h^c=h^60884 conjugacy classes — view the full character table.
| maximal subgroup of | #29591527, #29591529, #29591532, … |
| maximal normal subgroup of | #29591527, #29591529, #29591532, … |
| maximal quotient of | #29591559, #29591585, #29591618, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 6274);