Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #7453 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×#7454 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1365 |
| commutator | C2×C16 | C2×C4×C19 |
| Frattini, cosocle | C4×C16 | C22×C19 |
| prime radical | C22×C19 | #361 |
| LCS | G ▷ C2×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C4×C8×C19 ◁ C4×C16×C19 ◁ G | |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 2 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,31,49,33,44,30,25,52,50,62,55,61,47,81,28,34,45,66,26,53,46,63,27,32,51,65,43,68,23,42)(22,35,37,57,76,60,75,69,38,64,77,29,54,56,36,58,41,72,79,67,39,80,74,70,40,71,78,59,73,83,48,82);(20,22)(21,29,34,59)(23,37)(24,48)(25,40)(26,54)(27,38)(28,41)(30,60,63,80)(31,64,66,71)(32,67,52,57)(33,69,53,70)(35,65,72,62)(36,45)(39,55)(42,56,81,83)(43,76)(44,78)(46,77)(47,79)(49,73)(50,74)(51,75)(58,61,82,68)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 442);