Finite Group DatabasebetaFinite Group Databasebeta| order | 16380 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C32×C5×C7×C13 |
| multiplicative | (ℤ/16669)ˣ, (ℤ/16957)ˣ, (ℤ/19117)ˣ, (ℤ/24579)ˣ, (ℤ/33338)ˣ, (ℤ/33914)ˣ, (ℤ/38234)ˣ, (ℤ/49158)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
240 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 16380 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2)(5,6,7)(11,12,13,14,15)(16,17,18,19,20,21,22)(23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4)(8,9,10)16380 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16380, 333);