Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19651 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#19670 |
| 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 | |
746 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,25,28)(22,29,27,24)(23,26,31,33)(30,35,34,32)(36,37)(38,45)(39,44)(40,42)(41,49)(43,48)(46,50)(47,51);(20,22,24,21,25,27,29,28)(23,30,32,26,31,34,35,33)(37,42)(43,50)(44,49)(45,51);(20,23)(21,26)(22,30)(24,32)(25,31)(27,34)(28,33)(29,35)(36,38,41,48,40,47,39,46)(37,43,44,45,42,50,49,51);(23,31)(26,33)(30,34)(32,35)(36,39,40,41)(37,44,42,49)(38,46,47,48)(43,45,50,51)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12658);