Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10744 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | C22⋊#95 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1152 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,30,26,31,25,29)(22,32,34,27,35,42,36,41)(23,28,38,43,39,44,37,45)(33,47,50,51,49,46,48,40);(20,22,25,36,26,35,24,34)(21,27,30,42,31,41,29,32)(23,33,37,48,39,49,38,50)(28,40,43,47,44,51,45,46);(20,23)(21,28)(22,33)(24,38)(25,37)(26,39)(27,40)(29,45)(30,43)(31,44)(32,46)(34,50)(35,49)(36,48)(41,51)(42,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3732);