Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of D16 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#12556 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | D8 |
| commutator | C8 | C2×C42×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C23×C19 | C2×D8 |
| prime radical | C24×C19 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
606 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
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)(22,23)(24,25,26,27)(28,29)(30,41)(31,36)(32,38)(33,37)(34,40)(35,43)(39,47)(42,55)(44,49)(45,56)(46,53)(48,54)(50,58)(51,59)(52,57);(21,23)(28,30,33,44,31,42,46,57,34,45,48,59,47,58,32,43)(29,35,38,50,39,51,54,56,40,52,53,55,36,49,37,41);(28,31,34,47)(29,36,40,39)(30,42,45,58)(32,33,46,48)(35,49,52,51)(37,53,54,38)(41,55,56,50)(43,44,57,59)1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5544);