Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13015 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C2×D8 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
490 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25)(26,27)(28,29,32,38,48,57,46,35,34,40,31,37,33,39,49,53)(30,41,43,59,51,56,47,55,45,52,42,54,44,58,50,36);(20,21,22,23)(29,35)(31,46)(32,49)(33,48)(36,52)(37,39)(38,57)(40,53)(41,55)(42,47)(43,50)(44,51)(54,58)(56,59);(25,27)(28,30,34,45)(29,36,40,55)(31,47,32,50)(33,51,48,44)(35,52,53,41)(37,56,38,58)(39,59,57,54)(42,49,43,46)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6003);