Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23530 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#121 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1350 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(26,36)(27,41)(28,33)(29,34)(30,35)(31,39)(32,44)(37,46)(38,48)(40,47)(42,54)(43,50)(45,49)(51,52)(53,55);(24,26)(25,31)(27,42)(28,38)(29,39)(30,40)(32,46)(33,36)(34,47)(35,48)(37,45)(41,51)(43,53)(44,52)(49,55)(50,54);(21,23)(24,27,28,43,30,45,29,44)(25,32,34,49,35,50,33,41)(26,37,39,53,40,42,38,52)(31,46,36,51,48,54,47,55);(24,28,30,29)(25,33,35,34)(26,38,40,39)(27,43,45,44)(31,36,48,47)(32,41,50,49)(37,52,42,53)(46,51,54,55)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16518);