Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17547 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17615 |
| 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 | |
1038 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)(23,35)(27,39,42,50)(29,41,30,36)(32,46)(37,49)(43,51,44,47)(45,48);(20,21)(22,27)(23,36)(24,29)(25,30)(26,37)(28,38)(31,42)(32,47)(33,43)(34,44)(35,40)(39,48)(41,49)(45,51)(46,50);(20,22,24,33)(21,27,29,43)(23,32,35,46)(25,34,38,31)(26,39,41,51)(28,42,30,44)(36,47,40,50)(37,48,49,45);(22,31)(27,42)(32,45)(33,34)(39,50)(43,44)(46,48)(47,51)1159 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10603);