Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19572 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C23×C19 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
562 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(23,26)(27,31)(28,32)(30,33)(34,35)(36,37,41,45)(38,42,47,56)(39,49,51,59)(40,52,54,44)(43,53,58,50)(46,60,61,67)(48,64,63,57)(55,65,66,62);(20,21,26,32,24,28,23,25)(22,27,33,35,29,34,30,31)(36,38)(37,42)(39,46)(40,48)(41,47)(43,55)(44,57)(45,56)(49,60)(50,62)(51,61)(52,64)(53,65)(54,63)(58,66)(59,67);(20,22)(21,27)(23,30)(24,29)(25,31)(26,33)(28,34)(32,35)(36,39,41,51)(37,43,45,58)(38,46,47,61)(40,53,54,50)(42,55,56,66)(44,59,52,49)(48,65,63,62)(57,67,64,60);(21,28)(22,29)(25,32)(30,33)(38,47)(42,56)(46,61)(48,63)(55,66)(57,64)(60,67)(62,65)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12560);