Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18252 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18262 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3534 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1012 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)(20,21,25,23)(22,30,34,46)(24,37,39,49)(26,28,41,35)(27,42,31,32)(29,44,36,40)(33,45,48,50)(38,43,51,47);(20,22)(21,27)(23,31)(24,38)(25,34)(26,33)(28,43)(29,45)(30,37)(32,40)(35,47)(36,50)(39,51)(41,48)(42,44)(46,49);(20,23)(21,25)(22,31)(24,29)(26,35)(27,34)(28,41)(30,32)(33,47)(36,39)(37,40)(38,45)(42,46)(43,48)(44,49)(50,51);(21,28)(23,35)(27,43)(29,37)(30,45)(31,47)(36,49)(46,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11250);