Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1610 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,33)(23,39)(24,45)(25,49)(26,31)(27,32)(28,36)(29,43)(30,46)(34,62)(35,51)(37,53)(38,52)(40,60)(41,71)(42,57)(44,56)(47,59)(48,58)(50,64)(54,68)(55,74)(61,65)(63,80)(66,77)(67,76)(69,72)(70,75)(73,79)(78,83)(81,82);(20,22)(21,28)(23,40)(24,35)(25,37)(26,36)(27,38)(29,54)(30,51)(31,52)(32,53)(33,49)(34,42)(39,50)(41,70)(43,64)(44,68)(45,61)(46,67)(47,65)(48,66)(55,78)(56,62)(57,60)(58,76)(59,77)(63,73)(69,75)(71,80)(72,83)(74,82)(79,81);(20,23)(21,29)(22,34)(24,41)(25,42)(26,43)(27,44)(28,50)(30,55)(31,56)(32,57)(33,60)(35,63)(36,40)(37,68)(38,64)(39,49)(45,69)(46,72)(47,73)(48,74)(51,75)(52,54)(53,62)(58,79)(59,71)(61,80)(65,82)(66,83)(67,70)(76,78)(77,81);(20,24,27,48)(21,30,32,59)(22,35,38,66)(23,41,44,74)(25,47,26,46)(28,51,53,77)(29,55,57,71)(31,58,49,45)(33,61,52,76)(34,63,64,83)(36,67,37,65)(39,69,56,79)(40,70,68,82)(42,73,43,72)(50,75,62,81)(54,78,60,80)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16881);