Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#10800 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×C42 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #376 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ G | |
650 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)(26,35,38,49)(27,32)(28,33)(29,43)(30,34)(31,37,45,39)(36,48,51,55)(40,46)(41,53)(42,47)(44,50,54,52);(24,26,29,39,30,38,28,37)(25,31,33,35,34,45,43,49)(27,36,41,52,42,51,40,50)(32,44,46,48,47,54,53,55);(21,23)(24,27,28,40,30,42,29,41)(25,32,33,46,34,47,43,53)(26,36,37,50,38,51,39,52)(31,44,35,48,45,54,49,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3788);