Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#23820 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C23×C19 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C43×C19 ◁ G | |
726 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,26)(22,27,23,25)(28,29,31,33)(30,34,35,32)(36,37,39,42)(38,44,46,41)(40,43,47,50)(45,51,48,49);(20,22,24,23)(21,25,26,27)(28,30,31,35)(29,32,33,34)(38,45)(40,47)(41,49)(43,50)(44,51)(46,48);(29,33)(32,34)(36,38,39,46)(37,41,42,44)(40,48,47,45)(43,51,50,49);(20,23,24,22)(21,25,26,27)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16808);