Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33856 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33858 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | D4×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×C4×C19 ◁ C19×#443 ◁ G | |
668 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)(21,27)(22,32)(23,36)(24,25)(28,29)(30,46)(31,45)(33,50)(34,48)(35,41)(37,42)(39,40)(43,44)(47,49);(20,21,26,31)(22,33,35,28)(23,37,40,46)(24,30,25,42)(27,39,45,36)(29,48,50,34)(32,47,41,44)(38,49,51,43);(20,22)(21,28)(23,34)(24,41)(25,32)(26,35)(27,43)(29,46)(30,47)(31,33)(36,38)(37,50)(39,51)(40,48)(42,44)(45,49);(20,22)(21,29)(23,38)(24,32)(25,41)(26,35)(27,44)(28,46)(30,49)(31,50)(33,37)(34,36)(39,48)(40,51)(42,43)(45,47)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26846);