Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#19585 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
550 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)(20,21,25,29)(22,30,32,33)(23,27,26,35)(24,31,34,28)(36,37,41,45)(38,42,47,51)(39,44,40,49)(43,48,50,46);(20,22,24,27,25,32,34,35)(21,26,28,30,29,23,31,33)(36,38)(37,42)(39,48)(40,46)(41,47)(43,49)(44,50)(45,51);(20,23)(21,27)(22,31)(24,33)(25,26)(28,32)(29,35)(30,34)(36,38)(37,43)(39,46)(40,48)(41,47)(42,49)(44,51)(45,50);(22,32)(23,26)(27,35)(30,33)(36,39,41,40)(37,44,45,49)(38,46,47,48)(42,43,51,50)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12573);