Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9431 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#9431 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #386 |
| commutator | C42 | C22×C4×C19 |
| Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C19×#121 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
414 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 1216 |
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)(21,25)(22,28)(23,31)(27,33)(29,30)(32,34)(36,37)(38,45,46,49)(39,42,47,48)(40,43)(41,44)(50,51);(20,21,23,25,24,27,31,33)(22,26,29,32,30,35,28,34)(36,38,40,48,41,46,50,42)(37,39,43,49,44,47,51,45);(20,22)(21,26)(23,29)(24,30)(25,32)(27,35)(28,31)(33,34)(36,39)(37,42)(38,43)(40,49)(41,47)(44,48)(45,50)(46,51)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2419);