Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #13694 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#13733 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C19 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ C4×C8×C19 ◁ C4×C16×C19 ◁ G | |
158 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 3 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,25)(22,26,27,24)(29,34)(30,39)(31,40)(32,43)(35,42)(36,51)(37,54)(38,48)(41,50)(44,57)(45,46)(47,52)(49,58)(53,59)(55,56);(20,22,23,27)(21,24,25,26);(28,29,35,49,31,36,41,47,43,52,56,51,57,58,30,34,33,38,39,46,44,53,55,54,32,37,50,59,40,45,42,48)1330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6721);