Finite Group DatabasebetaFinite Group Databasebeta| order | 16770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((C13⋊C3)⋊D43) |
| unambiguous semidirect product | (C13⋊C3)⋊D215 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C43 | C2×C3 |
| LCS | G ▷ C5×C13×C43 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2795 |
Polycyclic presentation:
2,3,5,13,43|c^a=c^4,d^a=d^12,e^a=e^42,d^b=d^3757 conjugacy classes — view the full character table.
| maximal subgroup of | D43×C5⋊(D13⋊C3), D13⋊C3×D215, D5×(C13⋊C3)⋊D43, … |
| maximal normal subgroup of | D43×C5⋊(D13⋊C3), D13⋊C3×D215, D5×(C13⋊C3)⋊D43, … |
| maximal quotient of | #46776426, C2×C5⋊((C13⋊C3)⋊D43) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16770, 46);