Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2192 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13016 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #447 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1879 |
| prime radical | C2×C19×#508 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C4×C19 ◁ C19×#405 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,32,27,33,49,65,28,34,25,50,48,64,24,31)(22,35,39,58,40,63,37,66,41,69,38,29,53,56,51,57)(23,42,44,67,45,78,43,30,46,60,47,61,54,59,52,62)(36,70,72,77,73,55,75,68,74,81,79,83,76,82,71,80);(20,22,27,53,28,41,48,40)(21,29,33,66,34,58,64,57)(23,36,54,73,46,74,45,76)(24,38,26,37,49,39,25,51)(30,55,67,81,62,82,61,70)(31,63,32,35,65,56,50,69)(42,77,59,68,60,83,78,80)(43,72,44,75,52,79,47,71);(20,23)(21,30)(22,36)(24,47)(25,52)(26,43)(27,54)(28,46)(29,55)(31,42)(32,59)(33,67)(34,62)(35,68)(37,72)(38,71)(39,75)(40,76)(41,74)(44,49)(45,48)(50,78)(51,79)(53,73)(56,83)(57,70)(58,82)(60,65)(61,64)(63,77)(66,81)(69,80)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6004);