Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34490 |
| 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 | |
1840 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)(24,25,28,29)(26,32,33,30)(27,35,36,31)(34,37,39,38)(40,41,46,44)(42,49,43,47)(45,52,53,48)(50,54,51,55);(25,29)(26,33)(31,35)(34,39)(40,42,46,43)(41,47,44,49)(45,50,53,51)(48,54,52,55);(24,25)(26,30)(27,31)(28,29)(32,33)(34,37)(35,36)(38,39)(40,43,46,42)(41,47,44,49)(45,51,53,50)(48,54,52,55);(20,22,23,21)(24,26,28,33)(25,30,29,32)(27,34,36,39)(31,37,35,38)(40,44,46,41)(42,47,43,49)(45,52,53,48)(50,54,51,55);(24,27,28,36)(25,31,29,35)(26,34,33,39)(30,37,32,38)(40,45,46,53)(41,48,44,52)(42,50,43,51)(47,54,49,55)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27478);