Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#22691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
846 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)(26,38)(27,42)(28,34)(29,36)(30,35)(31,37)(32,40)(33,39)(41,54)(43,51)(44,52)(45,50)(46,55)(47,49)(48,53);(24,26)(25,32)(27,28)(29,43)(30,40)(31,41)(33,49)(34,52)(35,54)(36,38)(37,51)(39,46)(42,55)(44,48)(45,47)(50,53);(24,27,29,44,31,45,30,39)(25,33,35,50,37,52,36,42)(26,28,43,48,41,47,40,46)(32,49,54,53,51,34,38,55);(24,28)(25,34)(26,39)(27,43)(29,48)(30,46)(31,47)(32,50)(33,38)(35,55)(36,53)(37,49)(40,45)(41,44)(42,51)(52,54)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 15679);