Finite Group DatabasebetaFinite Group Databasebeta| order | 21450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | C11⋊#14519613 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C11×C13 | C2×C3 |
| LCS | G ▷ C52×C11×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2145 |
A minimal faithful permutation representation — 2 generators on 39 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26,28)(27,37,33,30,31,39)(29,34,38,35,36,32);(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,17,19,21,23,24,22,20,18,16)(25,27,32,38,30)(26,29,31,37,35)(28,33,34,36,39)Polycyclic presentation:
2,3,5^2,11,13|c^a=c^4,d^a=d^4,e^a=e^10,f^a=f^12,c^b=cd,d^b=c^2d^3791 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21450, 78);