Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#12916 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #120 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1850 |
| prime radical | C2×#41×C19 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C22×C8×C19 ◁ G | |
370 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)(20,21,25,31,26,30,45,56,27,32,46,57,24,41,44,58)(22,33,37,60,35,28,47,50,36,51,66,76,42,49,69,75)(23,29,39,53,38,54,67,78,40,55,68,79,43,52,70,77)(34,61,64,82,65,73,71,83,63,59,80,81,62,48,72,74);(20,22,25,37,26,35,45,47,27,36,46,66,24,42,44,69)(21,28,31,50,30,51,56,76,32,49,57,75,41,33,58,60)(23,34,39,64,38,65,67,71,40,63,68,80,43,62,70,72)(29,48,53,74,54,61,78,82,55,73,79,83,52,59,77,81);(20,23)(21,29)(22,34)(24,43)(25,39)(26,38)(27,40)(28,48)(30,54)(31,53)(32,55)(33,59)(35,65)(36,63)(37,64)(41,52)(42,62)(44,70)(45,67)(46,68)(47,71)(49,73)(50,74)(51,61)(56,78)(57,79)(58,77)(60,81)(66,80)(69,72)(75,83)(76,82)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5904);