Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#13164 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C19 | #121 |
| commutator | C2×C4 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1939 |
| prime radical | C23×C19 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C19 ◁ C22×C8×C19 ◁ G | |
284 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,31,26,30,41,48,27,32,40,29,24,42,23,39)(22,33,37,50,35,28,43,46,38,45,51,49,36,47,34,44);(20,22,25,37,26,35,41,43,27,38,40,51,24,36,23,34)(21,28,31,46,30,45,48,49,32,47,29,44,42,33,39,50);(20,23,24,40,27,41,26,25)(21,29,30,39,32,31,42,48)(22,34,36,51,38,43,35,37)(28,44,45,50,47,46,33,49)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6152);