Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10760 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #117 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C22×C19 | #380 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×M16×C19 ◁ G | |
1170 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)(24,25,28,35,30,34,29,33)(26,36,38,31,40,47,39,46)(27,41,43,49,44,32,42,48)(37,51,53,45,54,50,52,55);(21,23)(24,26,29,39,30,40,28,38)(25,31,35,47,34,46,33,36)(27,37,43,53,44,54,42,52)(32,45,49,51,41,55,48,50);(24,27)(25,32)(26,37)(28,42)(29,43)(30,44)(31,45)(33,48)(34,41)(35,49)(36,50)(38,52)(39,53)(40,54)(46,55)(47,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3748);