Finite Group DatabasebetaFinite Group Databasebeta| order | 15180 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic3795 |
| unambiguous semidirect product | C3⋊Dic1265 |
| unambiguous semidirect product | C11⋊Dic345 |
| unambiguous semidirect product | C23⋊Dic165 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3795 |
| commutator, hypocenter | C3×C5×C11×C23 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C11×C23 | C2 |
| LCS | G ▷ C3×C5×C11×C23 | |
| UCS | C1 ◁ C2 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 46 |
| transitive degree | μt(G) = 15180 |
A minimal faithful permutation representation — 2 generators on 46 points:
(1,2)(3,4)(5,6,7)(8,9,10,11,12)(13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(1,3,2,4)(6,7)(9,12)(10,11)(14,23)(15,22)(16,21)(17,20)(18,19)(25,46)(26,45)(27,44)(28,43)(29,42)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)Polycyclic presentation:
2,3,5,11,23,2|a^2=f,b^a=b^2,c^a=c^4,d^a=d^10,e^a=e^223798 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7590 |
| maximal normal subgroup of | Dic7590 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15180, 18);