Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D4×D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33950 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×Q8×C19 ◁ C8×Q8×C19 ◁ G | |
448 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,23)(22,26,27,25)(28,29,34,38)(30,35,33,48)(31,41,43,58)(32,44,47,57)(36,51,53,42)(37,40,55,46)(39,56,49,54)(45,50,59,52);(20,22,24,27)(21,25,23,26)(28,30,34,33)(29,35,38,48)(31,39,43,49)(32,40,47,46)(36,50,53,52)(37,44,55,57)(41,56,58,54)(42,45,51,59);(28,31,34,43)(29,36,38,53)(30,39,33,49)(32,45,47,59)(35,50,48,52)(37,54,55,56)(40,51,46,42)(41,57,58,44);(20,23,24,21)(22,25,27,26)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26938);