Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34530 |
| 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)(26,30)(27,34)(28,29)(31,35)(32,38)(33,36)(37,39)(40,41,45,48)(42,43,50,46)(44,52,53,47)(49,54,55,51);(25,29)(30,36)(31,34)(37,38)(40,42,45,50)(41,46,48,43)(44,49,53,55)(47,54,52,51);(20,21,23,22)(24,26,28,33)(25,30,29,36)(27,32,35,39)(31,37,34,38)(40,42)(41,46)(43,48)(44,49)(45,50)(47,54)(51,52)(53,55);(24,25)(26,30)(27,31)(28,29)(32,37)(33,36)(34,35)(38,39)(40,43,45,46)(41,42,48,50)(44,51,53,54)(47,49,52,55);(20,22,23,21)(24,27)(25,31)(26,32)(28,35)(29,34)(30,37)(33,39)(36,38)(40,44,45,53)(41,47,48,52)(42,49,50,55)(43,51,46,54)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27518);