Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21698 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C19×#376 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,27,26)(28,29,33,37)(30,38,42,52)(31,35,43,49)(32,45,39,36)(34,46,48,41)(40,51,54,59)(44,56,53,50)(47,57,58,55);(28,30,39,46,33,42,32,41)(29,34,45,52,37,48,36,38)(31,40,53,57,43,54,44,55)(35,47,56,59,49,58,50,51);(20,21,22,23)(28,31,33,43)(29,35,37,49)(30,40,42,54)(32,44,39,53)(34,47,48,58)(36,50,45,56)(38,51,52,59)(41,55,46,57);(24,26,27,25)(31,43)(35,49)(40,54)(44,53)(47,58)(50,56)(51,59)(55,57)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14686);