Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#33702 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3155 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
602 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25)(23,24)(26,27)(29,35)(30,40)(31,32)(33,44)(37,48)(38,49)(39,53)(41,42)(43,55)(45,46)(47,51)(52,58)(54,56)(57,59);(21,24)(25,27)(28,29,32,38,33,39,45,48,34,37,46,53,44,49,31,35)(30,36,40,51,42,52,54,57,43,50,55,59,56,58,41,47);(20,22,23,26)(21,25,24,27)(28,30,31,41,44,56,46,55,34,43,45,54,33,42,32,40)(29,36,35,47,49,58,53,59,37,50,48,57,39,52,38,51);(29,37)(35,48)(36,50)(38,53)(39,49)(47,57)(51,59)(52,58)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26690);