Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#17897 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C42 | C24×C19 |
| socle | C22×C19 | C2×C4×D4 |
| prime radical | C23×C19 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C19×#431 ◁ G | |
614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,22,23,25,27,26)(28,29)(30,38)(31,35)(32,44)(33,36)(34,40)(37,46)(39,52)(41,51)(42,50)(43,56)(45,48)(47,54)(49,55)(53,59)(57,58);(21,25)(22,26)(28,30,33,41)(29,34,36,48)(31,39,42,53)(32,45,46,40)(35,47,50,58)(37,51,44,38)(43,57,55,54)(49,59,56,52);(20,22,24,25,23,26,27,21)(28,31,33,42)(29,35,36,50)(30,39,41,53)(32,43,46,55)(34,47,48,58)(37,49,44,56)(38,52,51,59)(40,54,45,57);(29,36)(31,42)(34,48)(37,44)(38,51)(39,53)(43,55)(54,57)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10885);