Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#20954 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×#41×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
1694 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)(21,23)(24,25,29,35,30,33,28,34)(26,36,40,31,39,47,38,46)(27,41,43,48,44,32,42,49)(37,50,53,54,52,55,51,45);(20,21,22,23)(24,26)(25,31)(27,37)(28,40)(29,38)(30,39)(32,45)(33,46)(34,47)(35,36)(41,54)(42,53)(43,51)(44,52)(48,50)(49,55);(24,27,30,44)(25,32,33,41)(26,37,39,52)(28,43,29,42)(31,45,46,54)(34,49,35,48)(36,50,47,55)(38,53,40,51);(25,33)(31,46)(32,41)(34,35)(36,47)(45,54)(48,49)(50,55)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 13942);