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×#22459 |
| 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×#577 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
1312 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)(20,21,25,30,26,31,24,39)(22,32,35,27,36,45,40,44)(23,29,37,46,38,28,41,47)(33,49,34,42,51,43,50,48);(20,22,26,36)(21,27,31,44)(23,33,38,51)(24,40,25,35)(28,42,29,48)(30,45,39,32)(34,41,50,37)(43,46,49,47);(20,23)(21,28)(22,33)(24,37)(25,41)(26,38)(27,42)(29,31)(30,46)(32,43)(34,40)(35,50)(36,51)(39,47)(44,48)(45,49);(20,23)(21,29)(22,34)(24,41)(25,37)(26,38)(27,43)(28,31)(30,46)(32,42)(33,40)(35,51)(36,50)(39,47)(44,49)(45,48)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15447);