Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator | C8 | C23×C4×C19 |
| Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×#41×C19 | D4 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
658 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)(20,21,22,23)(25,30)(27,38)(28,39)(31,40)(32,41)(33,45)(34,44)(36,51)(37,50)(42,43)(46,49)(47,52)(48,55)(53,54);(24,25,31,45,28,33,27,30,29,34,38,43,39,42,40,44)(26,32,46,55,37,48,36,41,35,47,51,54,50,53,49,52);(24,26)(25,32)(27,36)(28,37)(29,35)(30,41)(31,46)(33,48)(34,47)(38,51)(39,50)(40,49)(42,53)(43,54)(44,52)(45,55);(26,35)(32,47)(36,49)(37,50)(41,52)(46,51)(48,53)(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, 26399);