Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10046 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10061 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
534 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,29,32)(26,33,35,38)(27,31,28,36)(30,37,39,34)(40,41,45,49)(42,50,53,54)(43,46,44,48)(47,51,55,52);(20,21)(22,23)(24,26,29,35)(25,30,32,39)(27,34,28,37)(31,38,36,33)(41,46)(43,44)(47,54)(48,49)(50,55)(51,52);(21,23)(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)(40,42,45,53)(41,47,49,55)(43,52,44,51)(46,54,48,50)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3049);