Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#17609 |
| 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×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C19×#117 ◁ G | |
944 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)(23,34)(27,39,43,50)(29,41,30,35)(32,47)(36,38)(42,48,44,51)(45,49);(20,21,24,29)(22,27,33,44)(23,35,34,40)(25,30,37,28)(26,38,41,36)(31,42,46,43)(32,48,47,50)(39,49,51,45);(20,22,24,33)(21,27,29,44)(23,32,34,47)(25,31,37,46)(26,39,41,51)(28,43,30,42)(35,48,40,50)(36,45,38,49);(22,31)(27,42)(32,45)(33,46)(39,48)(43,44)(47,49)(50,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10597);