Finite Group DatabasebetaFinite Group Databasebeta| order | 30660 |
| nilpotency class | 1 |
| automorphism | ? |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2 |
| abelian | C22×C3×C5×C7×C73 |
| multiplicative | (ℤ/31169)ˣ, (ℤ/33737)ˣ, (ℤ/45993)ˣ, (ℤ/61324)ˣ, (ℤ/62338)ˣ, (ℤ/67474)ˣ, (ℤ/91986)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) = 92 |
| transitive degree | μt(G) = 30660 |
A minimal faithful permutation representation — 2 generators on 92 points:
(1,2)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92);(3,4)30660 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30660, 49);