Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#21296 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
730 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)(28,29,33,37,34,38,32,47)(30,35,41,49,42,50,40,56)(31,43,46,51,44,57,45,36)(39,52,55,58,53,59,54,48);(21,24)(25,27)(28,30,33,41,34,42,32,40)(29,35,37,49,38,50,47,56)(31,39,46,55,44,53,45,54)(36,48,43,52,51,58,57,59);(28,31,32,45,34,44,33,46)(29,36,37,43,38,51,47,57)(30,39,40,54,42,53,41,55)(35,48,49,52,50,58,56,59);(20,22,23,26)(21,25,24,27)(31,44)(36,51)(39,53)(43,57)(45,46)(48,58)(52,59)(54,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14284);