Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#23365 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle, prime radical | C23×C19 | C23×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
636 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 4864 |
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)(22,26)(23,25)(24,27)(28,29,32,33,31,34,30,35)(36,37)(38,45)(39,43)(40,49)(41,44)(42,48)(46,51)(47,50);(22,27)(24,26)(36,38,41,48)(37,42,44,45)(39,47,40,46)(43,51,49,50);(20,22,23,27)(21,24,25,26)(28,30,31,32)(29,33,34,35)(36,39,41,40)(37,43,44,49)(38,46,48,47)(42,50,45,51);(21,25)(24,26)(36,40,41,39)(37,43,44,49)(38,47,48,46)(42,50,45,51)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16353);