Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9103 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10990 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1278 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)(20,21)(22,23)(24,25,29,33,30,34,28,43)(26,35,37,31,38,47,44,46)(27,39,41,50,42,32,40,49)(36,52,53,45,54,51,55,48);(24,26)(25,31)(27,36)(28,44)(29,37)(30,38)(32,48)(33,47)(34,46)(35,43)(39,45)(40,55)(41,53)(42,54)(49,52)(50,51);(21,23)(24,27,30,42)(25,32,34,39)(26,36,38,54)(28,41,29,40)(31,45,46,48)(33,50,43,49)(35,51,47,52)(37,55,44,53)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3978);