Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20955 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1710 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)(24,25,29,33,30,35,28,34)(26,36,38,31,40,46,39,47)(27,41,42,48,44,32,43,49)(37,50,53,54,52,55,51,45);(20,21,22,23)(24,26)(25,31)(27,37)(28,38)(29,39)(30,40)(32,45)(33,36)(34,46)(35,47)(41,54)(42,51)(43,53)(44,52)(48,50)(49,55);(24,27)(25,32)(26,37)(28,42)(29,43)(30,44)(31,45)(33,48)(34,49)(35,41)(36,50)(38,51)(39,53)(40,52)(46,55)(47,54);(24,28,30,29)(25,33,35,34)(26,38,40,39)(27,42,44,43)(31,36,47,46)(32,48,41,49)(37,51,52,53)(45,50,54,55)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13943);