Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C19 · Schur multiplier (H2) = C42 |
| direct product | C19×#12542 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C19 | C42 |
| commutator | C4 | C43×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1726 |
| prime radical | C23×C19 | #131 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C16×C19 ◁ G | |
350 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)(20,21,24,29,25,30,40,51,26,31,41,52,42,53,64,75)(22,27,33,44,35,46,57,68,34,45,56,67,58,69,77,81)(23,28,37,48,39,50,62,73,38,49,61,72,63,74,79,83)(32,43,54,65,36,47,59,70,55,66,76,80,60,71,78,82);(20,22)(21,27)(23,36,38,60)(24,33)(25,35)(26,34)(28,47,49,71)(29,44)(30,46)(31,45)(32,39,55,63)(37,59,61,78)(40,57)(41,56)(42,58)(43,50,66,74)(48,70,72,82)(51,68)(52,67)(53,69)(54,62,76,79)(64,77)(65,73,80,83)(75,81);(20,23)(21,28)(22,32,34,55)(24,37)(25,39)(26,38)(27,43,45,66)(29,48)(30,50)(31,49)(33,54,56,76)(35,36,58,60)(40,62)(41,61)(42,63)(44,65,67,80)(46,47,69,71)(51,73)(52,72)(53,74)(57,59,77,78)(64,79)(68,70,81,82)(75,83)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5530);