Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#17522 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C22×C22⋊C4 |
| prime radical | C19×#3481 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C4×#41×C19 ◁ G | |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(22,30)(23,28)(24,34)(25,29)(26,31)(27,32)(33,35)(36,37,40,45,41,43,39,44)(38,46,48,42,49,51,47,50);(20,22)(21,26)(23,31)(24,33)(25,32)(27,28)(29,35)(30,34)(36,38)(37,42)(39,47)(40,48)(41,49)(43,50)(44,46)(45,51);(20,22)(21,27)(23,33)(24,31)(25,32)(26,28)(29,30)(34,35)(37,43)(42,50)(44,45)(46,51);(20,23,25,24)(21,28,29,34)(22,31,32,33)(26,27,35,30)(36,39,41,40)(37,44,43,45)(38,47,49,48)(42,46,50,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10510);