Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24472 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24473 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #2410 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1314 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)(20,21,26,30,27,24,25,42)(22,31,34,28,36,45,35,33)(23,37,40,39,41,47,43,29)(32,49,50,46,51,44,38,48);(20,22)(21,28)(23,38)(24,33)(25,35)(26,34)(27,36)(29,46)(30,45)(31,42)(32,40)(37,44)(39,48)(41,50)(43,51)(47,49);(20,23)(21,29)(22,32)(24,39)(25,40)(26,43)(27,41)(28,44)(30,47)(31,48)(33,49)(34,38)(35,50)(36,51)(37,42)(45,46);(20,24,27,21)(22,33,36,28)(23,39,41,29)(25,30,26,42)(31,35,45,34)(32,49,51,44)(37,40,47,43)(38,48,50,46)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17461);