Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#22895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#454 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1008 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)(24,25,30,35)(26,36,39,52)(27,32,43,51)(28,34,29,33)(31,44,47,38)(37,54,41,48)(40,49,55,46)(42,53,45,50);(20,22,23,21)(24,26)(25,31)(27,40)(28,44)(29,38)(30,39)(32,48)(33,52)(34,36)(35,47)(37,42)(41,45)(43,55)(46,50)(49,53)(51,54);(24,26)(25,31)(27,41)(28,38)(29,44)(30,39)(32,49)(33,36)(34,52)(35,47)(37,43)(40,45)(42,55)(46,51)(48,53)(50,54);(24,27)(25,32)(26,37)(28,45)(29,42)(30,43)(31,46)(33,53)(34,50)(35,51)(36,54)(38,55)(39,41)(40,44)(47,49)(48,52)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15883);