Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C19 · Schur multiplier (H2) = C26×C4 |
| direct product | C19×#36821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C19 |
| prime radical | C19×#2431 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1776 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 5 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(22,26)(25,27)(29,33)(31,35)(37,41)(38,44)(43,48)(45,50);(21,24)(25,27)(29,33)(30,34)(36,37,40,41)(38,42,44,47)(39,43,46,48)(45,49,50,51);(20,21)(22,25)(23,24)(26,27)(28,29,32,33)(30,31,34,35)(36,37)(38,42)(39,43)(40,41)(44,47)(45,49)(46,48)(50,51);(20,21)(22,25)(23,24)(26,27)(28,30,32,34)(29,31,33,35)(36,38)(37,42)(39,45)(40,44)(41,47)(43,49)(46,50)(48,51);(20,22)(21,25)(23,26)(24,27)(28,31)(29,34)(30,33)(32,35)(36,39,40,46)(37,43,41,48)(38,45,44,50)(42,49,47,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 29809);