Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33551 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#33552 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C2×B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C24×C19 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C23×C19 ◁ C22×D4×C19 ◁ G | |
1156 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)(22,30)(23,27)(24,28)(25,29)(26,33)(31,43)(32,44)(34,40)(35,41)(36,49)(37,42)(38,46)(39,47)(45,51)(48,50);(20,22)(21,26)(23,31)(24,33)(25,32)(27,38)(28,30)(29,39)(34,46)(35,45)(36,48)(37,47)(40,43)(41,50)(42,44)(49,51);(20,23,25,35)(21,27,29,41)(22,31,32,45)(24,36,37,34)(26,38,39,50)(28,40,42,49)(30,43,44,51)(33,48,47,46);(22,32)(26,39)(30,44)(31,45)(33,47)(38,50)(43,51)(46,48)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26540);