Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33414 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C2×C19 | C22×#107 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
622 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)(22,33,37,58,39,59,38,67)(23,29,42,54,40,52,43,71)(24,44,45,55,46,72,34,30)(28,48,50,66,51,60,57,36)(35,56,64,79,62,77,65,82)(41,69,70,76,68,83,61,53)(49,73,75,81,74,80,78,63);(20,22,34,60,26,38,46,66,27,39,45,48,25,37,24,36)(21,28,44,58,31,50,55,59,32,51,72,67,47,57,30,33)(23,35,61,80,43,65,68,81,40,62,70,73,42,64,41,63)(29,49,69,79,54,75,76,77,52,74,83,82,71,78,53,56);(20,23)(21,29)(22,35)(24,41)(25,42)(26,43)(27,40)(28,49)(30,53)(31,54)(32,52)(33,56)(34,61)(36,63)(37,64)(38,65)(39,62)(44,69)(45,70)(46,68)(47,71)(48,73)(50,75)(51,74)(55,76)(57,78)(58,79)(59,77)(60,80)(66,81)(67,82)(72,83);(23,40)(29,52)(35,62)(41,68)(42,43)(49,74)(53,76)(54,71)(56,77)(61,70)(63,81)(64,65)(69,83)(73,80)(75,78)(79,82)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26402);