Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#21075 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#121 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
1014 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,35)(27,40)(28,33)(29,44)(30,34)(31,38)(32,43)(36,50)(37,46)(39,49)(41,55)(42,47)(45,51)(48,53)(52,54);(20,22,23,21)(24,26,29,38,30,39,28,37)(25,31,33,35,34,46,44,49)(27,36,42,52,43,53,41,51)(32,45,47,48,40,54,55,50);(24,27,29,42,30,43,28,41)(25,32,33,47,34,40,44,55)(26,36,38,52,39,53,37,51)(31,45,35,48,46,54,49,50);(24,28,30,29)(25,33,34,44)(26,37,39,38)(27,41,43,42)(31,35,46,49)(32,47,40,55)(36,51,53,52)(45,48,54,50)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14063);