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) = C26 |
| direct product | C19×#11015 |
| 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 | |
1242 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)(24,25,29,35,30,33,28,34)(26,36,39,46,40,31,38,47)(27,32,42,50,43,49,44,51)(37,52,41,55,53,45,54,48);(24,26,30,40)(25,31,33,36)(27,41,43,54)(28,39,29,38)(32,48,49,55)(34,47,35,46)(37,44,53,42)(45,51,52,50);(21,23)(24,27)(25,32)(26,37)(28,44)(29,42)(30,43)(31,45)(33,49)(34,51)(35,50)(36,52)(38,54)(39,41)(40,53)(46,55)(47,48)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4003);