Finite Group DatabasebetaFinite Group Databasebeta| order | 16770 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | D5×#13131976 |
| unambiguous semidirect product | C5⋊(C2×#13131976) |
| 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 |
756 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #46776457, #46776459, #46776467, … |
| maximal normal subgroup of | #46776457, #46776459, #46776467, … |
| maximal quotient of | Dic5×#13131976, C2×D5×#13131976 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16770, 35);