Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23882 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23883 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1696 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)(20,21)(22,32)(23,36)(24,29)(25,30)(26,31)(27,34)(28,38)(33,41)(35,46)(37,45)(39,44)(40,42)(43,49)(47,48)(50,51);(20,22)(21,27)(23,33)(24,40)(25,34)(26,35)(28,43)(29,32)(30,46)(31,42)(36,47)(37,50)(38,48)(39,49)(41,45)(44,51);(20,23,26,39)(21,28,31,45)(22,33,35,49)(24,38,25,37)(27,41,42,43)(29,44,30,36)(32,47,46,51)(34,50,40,48);(21,29)(24,25)(27,32)(28,44)(30,31)(34,40)(36,45)(37,38)(41,47)(42,46)(43,51)(48,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16871);