Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19728 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
690 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,26,31)(22,28,32,35)(23,27,33,34)(24,30,25,29)(38,44)(39,45)(41,47)(43,48)(46,50)(49,51);(20,22,25,33,26,32,24,23)(21,27,30,35,31,34,29,28)(36,37)(38,41)(39,43)(40,42)(44,47)(45,48)(46,49)(50,51);(20,23,24,32,26,33,25,22)(21,28,29,34,31,35,30,27)(36,38,45,50,40,46,39,44)(37,41,48,51,42,49,43,47);(22,32)(23,33)(27,34)(28,35)(37,42)(41,49)(43,48)(47,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12716);