Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17597 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17623 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3505 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×D4×C19 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,27,30,44)(22,33)(24,37)(28,46,47,49)(29,43,42,48)(31,45,32,40)(34,50)(36,38);(20,21)(22,28)(23,29)(24,40)(25,31)(26,32)(27,34)(30,41)(33,43)(35,49)(36,48)(37,44)(38,47)(39,46)(42,51)(45,50);(20,22)(21,28)(23,37)(24,35)(25,33)(26,36)(27,42)(29,44)(30,47)(31,43)(32,48)(34,51)(38,41)(39,50)(40,49)(45,46);(20,23,25,35)(21,29,31,49)(22,34,33,50)(24,38,37,36)(26,39,41,51)(27,43,45,28)(30,42,32,46)(40,47,44,48)931 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10611);