Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9091 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11059 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
842 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,29,35,30,33,28,34)(26,31,37,47,38,46,44,51)(27,39,42,49,43,32,41,50)(36,52,40,55,53,45,54,48);(20,21,22,23)(24,26)(25,31)(27,40)(28,44)(29,37)(30,38)(32,48)(33,46)(34,51)(35,47)(36,41)(39,55)(42,53)(43,54)(45,49)(50,52);(24,27,30,43)(25,32,33,39)(26,36,38,53)(28,42,29,41)(31,45,46,52)(34,50,35,49)(37,54,44,40)(47,55,51,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4047);