Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23412 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#392 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1948 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
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)(22,32)(23,37)(24,29)(25,30)(26,31)(27,35)(28,38)(33,41)(34,42)(36,46)(39,45)(40,44)(43,49)(47,48)(50,51);(20,22)(21,27)(23,33)(24,34)(25,35)(26,36)(28,43)(29,32)(30,46)(31,42)(37,47)(38,48)(39,50)(40,49)(41,45)(44,51);(20,23)(21,28)(22,33)(24,38)(25,39)(26,40)(27,41)(29,44)(30,37)(31,45)(32,47)(34,48)(35,50)(36,49)(42,43)(46,51);(20,24,26,25)(21,29,31,30)(22,34,36,35)(23,38,40,39)(27,32,42,46)(28,44,45,37)(33,48,49,50)(41,47,43,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16400);