Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21429 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
1010 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(22,25)(23,24)(26,27)(28,29,32,37,33,36,38,50)(30,34,41,46,40,47,44,51)(31,35,43,49,42,48,52,58)(39,45,54,57,53,56,55,59);(28,30,38,41,33,40,32,44)(29,34,37,51,36,47,50,46)(31,39,52,54,42,53,43,55)(35,45,49,59,48,56,58,57);(21,24)(25,27)(28,31,33,42)(29,35,36,48)(30,39,40,53)(32,43,38,52)(34,45,47,56)(37,49,50,58)(41,54,44,55)(46,57,51,59);(20,22,23,26)(21,25,24,27)(31,42)(35,48)(39,53)(43,52)(45,56)(49,58)(54,55)(57,59)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14417);