Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17367 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C28 |
| direct product | C19×#20593 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×C19×2−1+4 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×#41×C19 ◁ G | |
3594 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)(20,21)(22,23)(24,25,28,33,29,32,41,46)(26,34,36,47,37,30,40,43)(27,31,39,45,38,44,51,54)(35,48,50,55,49,42,52,53);(24,26,29,37)(25,30,32,34)(27,35,38,49)(28,40,41,36)(31,42,44,48)(33,47,46,43)(39,52,51,50)(45,55,54,53);(21,23)(24,27)(25,31)(26,35)(28,39)(29,38)(30,42)(32,44)(33,45)(34,48)(36,50)(37,49)(40,52)(41,51)(43,53)(46,54)(47,55);(27,38)(31,44)(35,49)(39,51)(42,48)(45,54)(50,52)(53,55)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13581);