Finite Group DatabasebetaFinite Group Databasebeta| order | 30940 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C5×C7×C13×C17 |
| multiplicative | (ℤ/31309)ˣ, (ℤ/31453)ˣ, (ℤ/62618)ˣ, (ℤ/62906)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
80 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 30940 |
A minimal faithful permutation representation — 2 generators on 46 points:
(1,2)(5,6,7,8,9)(10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29)(30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(3,4)30940 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30940, 17);