Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#17352 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×C22⋊C4 |
| commutator | C22 | C23×C8×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C4×Q8×C19 ◁ G | |
1162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(20,21,22,24,23,25,26,27)(28,29)(30,38,41,34)(31,35)(32,36)(33,37)(39,52,55,46)(40,53,57,47)(42,48)(43,49)(44,50)(45,51)(54,59,56,58);(28,30)(29,34)(31,39)(32,40)(33,41)(35,46)(36,47)(37,38)(42,54)(43,55)(44,56)(45,57)(48,58)(49,52)(50,59)(51,53);(28,31,33,43)(29,35,37,49)(30,39,41,55)(32,44,45,42)(34,46,38,52)(36,50,51,48)(40,56,57,54)(47,59,53,58);(28,32,33,45)(29,36,37,51)(30,40,41,57)(31,42,43,44)(34,47,38,53)(35,48,49,50)(39,54,55,56)(46,58,52,59)1558 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 10340);