Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7734 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#7794 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
394 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29)(30,32)(31,34)(33,35)(36,37,40,43)(38,41,45,48)(39,42,46,49)(44,50,51,47);(20,21,23,25)(22,27,26,24)(36,38)(37,41)(39,44)(40,45)(42,47)(43,48)(46,51)(49,50);(29,32)(30,35)(33,34)(36,39,40,46)(37,42,43,49)(38,44,45,51)(41,47,48,50)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 782);