Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34526 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1800 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 5 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,32)(27,29)(28,35)(30,33)(31,36)(34,37)(38,39)(40,41,44,47)(42,48,50,45)(43,46,51,53)(49,54,55,52);(25,27)(26,33)(31,35)(34,39)(40,41,44,47)(42,45,50,48)(43,46,51,53)(49,52,55,54);(20,21,23,22)(24,26)(25,30)(27,32)(28,34)(29,33)(31,37)(35,38)(36,39)(40,41)(42,45)(43,46)(44,47)(48,50)(49,52)(51,53)(54,55);(24,27,29,25)(26,32,33,30)(28,35,36,31)(34,38,39,37)(40,42)(41,45)(43,49)(44,50)(46,52)(47,48)(51,55)(53,54);(20,22,23,21)(24,28)(25,31)(26,34)(27,35)(29,36)(30,37)(32,38)(33,39)(40,43,44,51)(41,46,47,53)(42,49,50,55)(45,52,48,54)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27514);