Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#24772 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
840 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
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)(21,22)(24,25,28,33,30,35,29,34)(26,31,37,46,38,47,44,51)(27,39,41,50,43,49,42,32)(36,48,40,54,52,55,53,45);(20,21,23,22)(24,26)(25,31)(27,40)(28,37)(29,44)(30,38)(32,48)(33,46)(34,51)(35,47)(36,42)(39,54)(41,52)(43,53)(45,49)(50,55);(24,27,30,43)(25,32,35,50)(26,36,38,52)(28,42,29,41)(31,45,47,54)(33,49,34,39)(37,53,44,40)(46,55,51,48);(20,22,23,21)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 17760);