Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#21240 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C22×C19×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×M16×C19 ◁ G | |
1466 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,29,33,30,34,28,44)(26,35,39,46,37,49,38,31)(27,40,42,47,43,54,41,32)(36,50,53,55,51,45,52,48);(20,21,22,23)(24,26)(25,31,34,46)(27,36)(28,38)(29,39)(30,37)(32,45,47,50)(33,35,44,49)(40,48,54,55)(41,52)(42,53)(43,51);(24,27,28,41,30,43,29,42)(25,32,33,40,34,47,44,54)(26,36,38,52,37,51,39,53)(31,45,35,48,46,50,49,55);(26,37)(31,46)(35,49)(36,51)(38,39)(45,50)(48,55)(52,53)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14228);