Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8479 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#8488 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #379 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C19×#3535 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
768 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(20,21)(22,23,27,25)(24,26)(28,29,33,38,34,39,32,37)(30,40,44,35,43,50,42,49)(31,36,45,51,46,52,47,53)(41,55,56,59,57,54,58,48);(20,22)(21,25)(23,26)(24,27)(28,30)(29,35)(31,41)(32,44)(33,42)(34,43)(36,48)(37,50)(38,40)(39,49)(45,58)(46,57)(47,56)(51,54)(52,59)(53,55);(20,23,24,25)(21,22,26,27)(28,31)(29,36)(30,41)(32,47)(33,45)(34,46)(35,48)(37,53)(38,51)(39,52)(40,54)(42,58)(43,57)(44,56)(49,59)(50,55)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 1476);