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×#10799 |
| 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)(26,34,37,47)(27,31)(28,32)(29,33)(30,36,42,50)(35,46,49,54)(38,43)(39,44)(40,45)(41,48,52,55)(51,53);(24,26)(25,30,33,42)(27,35)(28,36)(29,37)(31,41,44,52)(32,34,45,47)(38,48)(39,49)(40,50)(43,46,53,54)(51,55);(21,23)(24,27,28,38,29,39,40,51)(25,31,32,43,33,44,45,53)(26,35,36,48,37,49,50,55)(30,41,34,46,42,52,47,54)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3787);