Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#20787 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #117 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C2×C19 | #2283 |
| prime radical | C2×#41×C19 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C19×#405 ◁ G | |
616 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)(22,31,34,27)(23,28)(24,29)(25,30)(26,33,39,47)(32,44,46,40)(35,41)(36,42)(37,43)(38,45,49,51)(48,50);(20,22)(21,26,30,39)(23,32)(24,33)(25,34)(27,29,31,43)(28,38,42,49)(35,45)(36,46)(37,47)(40,41,44,50)(48,51);(20,22)(21,27)(23,32)(24,33)(25,34)(26,29)(28,40)(30,31)(35,45)(36,46)(37,47)(38,41)(39,43)(42,44)(48,51)(49,50);(20,23,24,35,25,36,37,48)(21,28,29,41,30,42,43,50)(22,32,33,45,34,46,47,51)(26,38,31,44,39,49,27,40)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13775);