Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10218 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10224 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #127 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(20,21,26,30)(22,31,23,34)(24,29,25,28)(27,33,35,32)(38,45)(39,40)(42,46)(43,49)(47,48)(50,51);(20,22,26,23)(21,27,30,35)(24,33,25,32)(28,34,29,31)(36,37)(38,46)(39,43)(40,49)(41,44)(42,48)(45,50)(47,51);(20,23,26,22)(21,27,30,35)(24,32,25,33)(28,34,29,31)(36,38)(37,42)(39,48)(40,45)(41,47)(43,51)(44,50)(46,49)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3212);