Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34372 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C24×C19 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1910 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
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)(20,21,22,23)(24,25,29,27)(26,30,34,32)(28,35,36,31)(33,38,39,37)(41,45)(42,48)(43,51)(53,55);(25,27)(30,32)(31,35)(37,38)(40,41,44,45)(42,49,48,46)(43,47,51,52)(50,55,54,53);(24,26,29,34)(25,30,27,32)(28,33,36,39)(31,37,35,38)(40,41)(42,46)(43,47)(44,45)(48,49)(50,53)(51,52)(54,55);(24,27,29,25)(26,32,34,30)(28,35,36,31)(33,38,39,37)(40,42,44,48)(41,46,45,49)(43,50,51,54)(47,53,52,55);(24,28)(25,31)(26,33)(27,35)(29,36)(30,37)(32,38)(34,39)(40,43)(41,47)(42,50)(44,51)(45,52)(46,53)(48,54)(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, 27360);