Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#10743 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #386 |
| commutator | C2×C4 | C2×C42×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle | C2×C19 | C22⋊#95 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C23×C4×C19 ◁ G | |
1208 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)(20,21,25,29,26,30,24,38)(22,31,35,41,34,46,33,27)(23,28,36,43,37,44,39,42)(32,47,48,40,49,45,50,51);(20,22)(21,27,30,41)(23,32)(24,33)(25,35)(26,34)(28,40,44,51)(29,31,38,46)(36,48)(37,49)(39,50)(42,47,43,45);(20,23)(21,28)(22,32)(24,39)(25,36)(26,37)(27,40)(29,43)(30,44)(31,45)(33,50)(34,49)(35,48)(38,42)(41,51)(46,47)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3731);