Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19091 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3561 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
854 conjugacy classes of subgroups.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 67 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,28)(23,31)(24,26)(25,30)(27,32)(29,35)(33,34)(36,37,42,47)(38,48,51,58)(39,52,54,60)(40,45,41,46)(43,55,59,50)(44,56,61,53)(49,57,65,67)(62,63,66,64);(23,32)(27,31)(28,35)(30,33)(36,38,42,51)(37,43,47,59)(39,49,54,65)(40,55,41,50)(44,57,61,67)(45,48,46,58)(52,66,60,62)(53,64,56,63);(20,22)(21,25)(23,33)(24,29)(26,34)(27,35)(28,31)(30,32)(36,39)(37,44)(38,49)(40,53)(41,56)(42,54)(43,57)(45,60)(46,52)(47,61)(48,62)(50,63)(51,65)(55,64)(58,66)(59,67);(21,26)(25,34)(27,31)(28,35)(36,40,42,41)(37,45,47,46)(38,50,51,55)(39,53,54,56)(43,58,59,48)(44,60,61,52)(49,63,65,64)(57,66,67,62)589 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12079);