Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#34507 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C25 |
| commutator | C22 | C24×C4×C19 |
| Frattini, cosocle | C23 | C25×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
1924 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)(20,21,23,22)(25,29)(26,32)(31,36)(33,38)(40,41,46,48)(42,49,43,44)(45,53,54,47)(50,52,51,55);(25,29)(30,35)(31,36)(37,39)(40,42,46,43)(41,44,48,49)(45,50,54,51)(47,52,53,55);(24,25)(26,30)(27,31)(28,29)(32,35)(33,37)(34,36)(38,39)(40,43,46,42)(41,44,48,49)(45,51,54,50)(47,52,53,55);(20,22,23,21)(24,26)(25,30)(27,33)(28,32)(29,35)(31,37)(34,38)(36,39)(40,44)(41,42)(43,48)(45,52)(46,49)(47,50)(51,53)(54,55);(24,27,28,34)(25,31,29,36)(26,33,32,38)(30,37,35,39)(40,45,46,54)(41,47,48,53)(42,50,43,51)(44,52,49,55)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 27495);