Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33388 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33388 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×#102 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3584 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
1128 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)(21,26,28,40)(23,33)(24,36)(27,39,42,50)(29,34,37,41)(31,46)(32,45)(35,38)(43,47,48,51)(44,49);(20,21)(22,27)(23,34)(24,37)(25,28)(26,38)(29,36)(30,42)(31,47)(32,48)(33,40)(35,41)(39,49)(43,45)(44,51)(46,50);(20,22)(21,27)(23,31)(24,32)(25,30)(26,39)(28,42)(29,43)(33,46)(34,47)(35,44)(36,45)(37,48)(38,49)(40,50)(41,51);(22,30)(27,42)(31,44)(32,45)(39,50)(43,48)(46,49)(47,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26376);