Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#25189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
1000 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)(24,25,30,34,31,35,29,45)(26,36,38,32,27,39,41,48)(28,42,43,33,44,49,46,50)(37,47,53,54,40,55,52,51);(20,21)(22,23)(24,26,30,38,31,27,29,41)(25,32,34,39,35,48,45,36)(28,37,43,53,44,40,46,52)(33,47,49,54,50,55,42,51);(21,23)(24,27)(25,32)(26,31)(28,40)(29,41)(30,38)(33,47)(34,36)(35,48)(37,44)(39,45)(42,54)(43,53)(46,52)(49,51)(50,55);(24,28,31,44)(25,33,35,50)(26,37,27,40)(29,46,30,43)(32,47,48,55)(34,49,45,42)(36,51,39,54)(38,53,41,52)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 18177);