Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #22455 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#22455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | D4×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#576 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1378 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)(23,35,37,27)(24,38)(25,29)(26,33)(28,39)(31,45,48,44)(32,42)(34,41)(36,43,51,50)(40,47,49,46);(20,22)(21,26)(23,31)(24,32)(25,34)(27,40)(28,41)(29,42)(30,38)(33,39)(35,49)(36,46)(37,48)(43,45)(44,50)(47,51);(20,23)(21,27)(22,31)(24,36)(25,37)(26,40)(28,43)(29,35)(30,44)(32,46)(33,47)(34,48)(38,50)(39,51)(41,45)(42,49);(22,32)(24,39)(26,41)(28,38)(30,42)(31,46)(33,34)(36,51)(40,45)(43,50)(44,49)(47,48)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15443);