Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#20713 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #381 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | C2×#381 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1244 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)(20,21,25,31,26,30,24,29)(22,32,34,45,35,27,40,42)(23,36,39,43,38,28,37,44)(33,41,47,50,48,46,49,51);(20,22)(21,27)(23,33)(24,34)(25,40)(26,35)(28,41)(29,42)(30,32)(31,45)(36,46)(37,47)(38,48)(39,49)(43,50)(44,51);(20,23)(21,28,30,36)(22,33)(24,37)(25,39)(26,38)(27,41,32,46)(29,43,31,44)(34,47)(35,48)(40,49)(42,50,45,51);(20,24,26,25)(21,29,30,31)(22,34,35,40)(23,37,38,39)(27,42,32,45)(28,43,36,44)(33,47,48,49)(41,50,46,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13701);