Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20962 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1742 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)(21,23)(24,25)(26,30)(27,37,39,31)(28,40)(29,33)(32,41)(34,42,47,50)(35,48)(36,44)(38,45,52,51)(43,49)(46,54,55,53);(20,21,22,23)(24,26,29,36)(25,30,33,44)(27,34,39,47)(28,35,41,49)(31,42,37,50)(32,43,40,48)(38,46,52,55)(45,53,51,54);(24,27)(25,31)(26,34)(28,38)(29,39)(30,42)(32,45)(33,37)(35,46)(36,47)(40,51)(41,52)(43,53)(44,50)(48,54)(49,55);(24,28,29,41)(25,32,33,40)(26,35,36,49)(27,38,39,52)(30,43,44,48)(31,45,37,51)(34,46,47,55)(42,53,50,54)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13950);