Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23439 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#23522 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(26,34)(27,38)(28,42)(29,32)(30,36)(31,41)(33,44)(35,51)(37,49)(39,50)(40,48)(43,46)(45,54)(47,52)(53,55);(24,26,29,37)(25,30,32,46)(27,39,41,35)(28,43,44,36)(31,47,38,45)(33,49,42,34)(40,52,55,54)(48,50,53,51);(21,23)(24,27,28,40,29,41,44,55)(25,31,33,48,32,38,42,53)(26,35,36,52,37,39,43,54)(30,45,34,50,46,47,49,51);(25,32)(30,46)(31,38)(33,42)(34,49)(45,47)(48,53)(50,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16510);