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×#33867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3285 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(20,21,23,25)(22,26,27,24)(28,29)(30,35)(31,41)(32,44)(33,48)(34,38)(36,42)(37,46)(39,55)(40,54)(43,58)(45,50)(47,57)(49,53)(51,59)(52,56);(20,22)(21,24)(23,27)(25,26)(28,30,34,33)(29,35,38,48)(31,39,43,49)(32,40,47,46)(36,50,52,51)(37,44,54,57)(41,55,58,53)(42,45,56,59);(28,31,34,43)(29,36,38,52)(30,39,33,49)(32,45,47,59)(35,50,48,51)(37,53,54,55)(40,56,46,42)(41,57,58,44);(22,27)(24,26)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26855);