Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C61 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D61 |
| commutator, hypocenter | C61 | C128 |
| Fitting | C61×C64 | C2 |
| socle | C2×C61 | C64 |
| LCS | G ▷ C61 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^602048 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D61×C128, C2×#21443638, #29567923, … |
| maximal normal subgroup of | D61×C128, C2×#21443638, #29567923, … |
| maximal quotient of | #29566538, C2×#21443638 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2329);