Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18446 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18457 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3536 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,26,31)(22,32,23,28)(24,30,25,29)(27,34,35,33)(36,37)(38,41)(39,42)(40,43)(44,50)(45,48)(46,49)(47,51);(20,22,26,23)(21,27,31,35)(24,33,25,34)(28,29,32,30)(36,38)(37,41)(39,44)(40,45)(42,47)(43,48)(46,51)(49,50);(20,23,26,22)(21,28,31,32)(24,33,25,34)(27,29,35,30)(36,39)(37,42)(38,44)(40,46)(41,47)(43,49)(45,51)(48,50);(20,24,26,25)(21,29,31,30)(22,33,23,34)(27,32,35,28)(37,43)(41,48)(42,49)(47,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11445);