Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#18079 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C19×#121 | C2×C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×M16×C19 ◁ G | |
588 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
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)(20,21,24,26)(22,28,30,35)(23,31,33,27)(25,32,34,29)(36,37,41,44,42,38,40,46)(39,43,49,50,47,45,48,51);(20,22,24,30)(21,25,26,34)(23,32,33,29)(27,35,31,28)(36,38,42,37)(39,45,47,43)(40,44,41,46)(48,50,49,51);(36,39,40,48,42,47,41,49)(37,43,46,51,38,45,44,50);(21,26)(25,34)(27,31)(28,35)(37,38)(39,47)(44,46)(48,49)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11067);