Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#21737 |
| 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 | C23×C19 | C2×#41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C4×C8×C19 ◁ G | |
662 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)(22,27)(23,25)(24,26)(28,29,35,39,33,38,34,50)(30,40,45,55,43,36,44,53)(31,46,49,54,48,58,32,37)(41,56,42,51,47,59,57,52);(20,22,24,23)(21,25,26,27)(28,30,33,43)(29,36,38,40)(31,47,48,41)(32,42,49,57)(34,44,35,45)(37,52,54,51)(39,53,50,55)(46,56,58,59);(28,31,34,32,33,48,35,49)(29,37,39,46,38,54,50,58)(30,41,44,57,43,47,45,42)(36,51,53,59,40,52,55,56);(20,23,24,22)(21,25,26,27)(28,32,34,48,33,49,35,31)(29,37,50,58,38,54,39,46)(30,42,44,41,43,57,45,47)(36,52,55,59,40,51,53,56)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14725);