Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33607 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33740 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
532 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(30,38)(31,39)(32,42)(34,44)(36,45)(37,49)(40,54)(41,52)(43,53)(46,55)(47,59)(48,58)(50,51)(56,57);(21,24)(25,27)(28,29,33,35)(30,34,41,46)(31,36,43,48)(32,37,42,49)(38,44,52,55)(39,45,53,58)(40,47,50,56)(51,57,54,59);(28,30,39,51,32,40,43,52,33,41,53,54,42,50,31,38)(29,34,45,57,37,47,48,55,35,46,58,59,49,56,36,44);(20,22,23,26)(21,25,24,27)(29,35)(34,46)(36,48)(37,49)(44,55)(45,58)(47,56)(57,59)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26728);