Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20998 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#386 |
| prime radical | C2×C19×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1704 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)(20,21,25,30,26,31,24,29)(22,32,35,43,36,42,34,27)(23,37,38,28,40,44,39,45)(33,41,47,50,49,51,48,46);(20,22)(21,27,31,43)(23,33)(24,34)(25,35)(26,36)(28,41,45,51)(29,42,30,32)(37,46,44,50)(38,47)(39,48)(40,49);(20,23)(21,28)(22,33)(24,38)(25,39)(26,40)(27,41)(29,44)(30,37)(31,45)(32,46)(34,47)(35,48)(36,49)(42,50)(43,51);(20,24,26,25)(21,29,31,30)(22,34,36,35)(23,38,40,39)(27,42,43,32)(28,44,45,37)(33,47,49,48)(41,50,51,46)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13986);