Finite Group DatabasebetaFinite Group Databasebeta| order | 7770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊#13095536 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C37 | C2×C3 |
| LCS | G ▷ C5×C7×C37 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,37|c^a=c^4,d^a=d^6,d^b=d^2,e^b=e^10245 conjugacy classes — view the full character table.
| maximal subgroup of | #13095532⋊D5, #13095538⋊D5, D5×#13095536, … |
| maximal normal subgroup of | #13095532⋊D5, #13095538⋊D5, D5×#13095536, … |
| maximal quotient of | #29509542, C2×C5⋊#13095536, C5⋊#17987936, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7770, 44);