Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19713 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C8 |
| direct product | C19×#19729 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
788 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,25)(23,26)(27,31)(28,32)(30,33)(34,35)(36,37)(38,46)(39,42)(40,50)(41,45)(43,48)(44,47)(49,51);(20,21,26,32,24,28,23,25)(22,27,33,35,29,34,30,31)(36,38,47,49,41,48,40,39)(37,42,50,43,45,51,44,46);(20,22,24,29)(21,27,28,34)(23,30,26,33)(25,31,32,35)(36,39,40,48,41,49,47,38)(37,43,44,42,45,46,50,51);(22,29)(27,34)(30,33)(31,35)(38,48)(39,49)(42,51)(43,46)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12717);