Finite Group DatabasebetaFinite Group Databasebeta| order | 7808 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C61 ⋊ #1397 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C16 | C2×D61 |
| commutator | C2×C61 | C4×C16 |
| Fitting | C2×C32×C61 | C2 |
| socle | C22×C61 | C2×C16 |
| hypercenter | C2×C32 | D61 |
| hypocenter | C61 | #1397 |
| LCS | G ▷ C2×C61 ▷ C61 | |
| UCS | C1 ◁ C2×C16 ◁ C2×C32 | |
68 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,61|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bg,h^b=h^602000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #29567819, D61×#1397, C2×#21443952, … |
| maximal normal subgroup of | #29567819, D61×#1397, C2×#21443952, … |
| maximal quotient of | #29567340, #29567345, #29567699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7808, 2643);