Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10277 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
510 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)(20,21)(22,23)(24,25,29,33)(26,34,37,38)(27,32,28,31)(30,36,39,35)(40,41,44,47)(42,48,50,55)(43,51,53,46)(45,52,54,49);(21,23)(24,26,29,37)(25,30,33,39)(27,36,28,35)(31,38,32,34);(26,35)(27,28)(30,34)(31,32)(36,37)(38,39)(40,42,44,50)(41,45,47,54)(43,52,53,49)(46,55,51,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3265);