Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#12989 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C23 | C22×C8×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| socle | C2×C19 | #1869 |
| prime radical | C19×#525 | C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C22×C8×C19 ◁ G | |
470 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)(20,21,24,29,25,30,38,44,26,22,27,32,39,33,40,46)(23,31,35,43,36,45,48,51,34,28,37,41,47,42,49,50);(20,22,24,29,25,33,38,44,26,21,27,32,39,30,40,46)(23,31,37,43,36,45,49,51,34,28,35,41,47,42,48,50);(20,23)(21,28)(22,31)(24,37)(25,36)(26,34)(27,35)(29,43)(30,42)(32,41)(33,45)(38,49)(39,47)(40,48)(44,51)(46,50)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 5977);