Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33459 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#508 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
674 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
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)(20,21,23,22)(24,25)(26,32)(27,35)(28,42)(29,33)(30,36)(31,38)(34,44)(37,51)(39,50)(40,48)(41,53)(43,49)(45,52)(46,55)(47,54);(24,26)(25,31)(27,37)(28,43)(29,40)(30,39)(32,42)(33,46)(34,48)(35,49)(36,47)(38,44)(41,54)(45,55)(50,52)(51,53);(20,22,23,21)(24,26)(25,32)(27,40)(28,38)(29,37)(30,39)(31,42)(33,51)(34,49)(35,48)(36,50)(41,55)(43,44)(45,54)(46,53)(47,52);(24,27,30,29)(25,33,36,35)(26,37,39,40)(28,41,45,44)(31,46,47,49)(32,48,50,51)(34,52,53,42)(38,43,54,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26447);