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×#33870 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
558 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)(28,29,34,38)(30,35,33,48)(31,41,43,57)(32,44,47,58)(36,51,53,42)(37,40,55,46)(39,56,49,54)(45,50,59,52);(20,22)(21,24)(23,27)(25,26)(28,30,34,33)(29,35,38,48)(31,39,43,49)(32,40,47,46)(36,50,53,52)(37,44,55,58)(41,56,57,54)(42,45,51,59);(28,31)(29,36)(30,39)(32,45)(33,49)(34,43)(35,50)(37,54)(38,53)(40,51)(41,44)(42,46)(47,59)(48,52)(55,56)(57,58);(22,27)(24,26)(28,30,34,33)(29,35,38,48)(31,39,43,49)(32,40,47,46)(36,50,53,52)(37,44,55,58)(41,56,57,54)(42,45,51,59)1045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26858);