Finite Group DatabasebetaFinite Group Databasebeta| order | 1976 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 36288 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C13×C19 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 1976 |
A minimal faithful permutation representation — 3 generators on 38 points:
(1,2)(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);(3,4);(5,6)1976 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1976, 39);