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×#33856 |
| 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 | |
652 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)(33,49)(34,50)(35,41)(37,42)(39,40)(43,44)(47,48);(20,21)(22,33)(23,37)(24,30)(25,42)(26,31)(27,36)(28,35)(29,34)(32,47)(38,48)(39,45)(40,46)(41,44)(43,51)(49,50);(20,22)(21,28)(23,34)(24,41)(25,32)(26,35)(27,43)(29,46)(30,47)(31,33)(36,38)(37,49)(39,51)(40,50)(42,44)(45,48);(20,22)(21,29)(23,38)(24,32)(25,41)(26,35)(27,44)(28,46)(30,48)(31,49)(33,37)(34,36)(39,50)(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, 26844);