Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33404 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33404 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#106 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
636 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)(21,26,28,37)(23,33)(24,35)(27,36,39,47)(29,42,41,38)(31,45)(32,44)(34,46)(40,50,49,48)(43,51);(20,21,23,26,24,29,33,38,25,28,34,37,35,41,46,42)(22,27,31,36,32,40,45,48,30,39,43,47,44,49,51,50);(20,22)(21,27)(23,31)(24,32)(25,30)(26,36)(28,39)(29,40)(33,45)(34,43)(35,44)(37,47)(38,48)(41,49)(42,50)(46,51);(22,30)(27,39)(31,43)(32,44)(36,47)(40,49)(45,51)(48,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26392);