Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24468 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#24470 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#3489 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1360 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)(24,25,30,35,31,36,29,45)(26,37,28,32,39,34,44,48)(27,40,42,51,43,50,46,33)(38,53,54,49,55,47,41,52);(20,21)(22,23)(24,26)(25,32)(27,38)(28,30)(29,44)(31,39)(33,47)(34,35)(36,48)(37,45)(40,52)(41,46)(42,54)(43,55)(49,50)(51,53);(21,23)(24,27,31,43)(25,33,36,51)(26,38,39,55)(28,41,44,54)(29,42,30,46)(32,47,48,53)(34,49,37,52)(35,50,45,40);(24,28)(25,34)(26,29)(27,41)(30,39)(31,44)(32,45)(33,49)(35,48)(36,37)(38,42)(40,47)(43,54)(46,55)(50,53)(51,52)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17458);