Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33385 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C22×#102 |
| prime radical | C19×#3584 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
1114 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)(20,21,25,31,27,32,26,47)(22,33,36,59,37,60,48,56)(23,29,40,55,38,53,41,70)(24,42,44,57,46,72,45,30)(28,43,50,64,52,73,51,35)(34,58,63,80,61,79,71,78)(39,66,68,77,65,82,69,54)(49,67,75,81,74,83,76,62);(20,22)(21,28)(23,34)(24,43)(25,36)(26,48)(27,37)(29,49)(30,56)(31,50)(32,52)(33,42)(35,45)(38,61)(39,67)(40,63)(41,71)(44,64)(46,73)(47,51)(53,74)(54,78)(55,75)(57,59)(58,66)(60,72)(62,69)(65,83)(68,81)(70,76)(77,80)(79,82);(20,23)(21,29)(22,34)(24,39)(25,40)(26,41)(27,38)(28,49)(30,54)(31,55)(32,53)(33,58)(35,62)(36,63)(37,61)(42,66)(43,67)(44,68)(45,69)(46,65)(47,70)(48,71)(50,75)(51,76)(52,74)(56,78)(57,77)(59,80)(60,79)(64,81)(72,82)(73,83);(23,38)(29,53)(34,61)(39,65)(40,41)(49,74)(54,77)(55,70)(58,79)(62,81)(63,71)(66,82)(67,83)(68,69)(75,76)(78,80)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26373);