Finite Group DatabasebetaFinite Group Databasebeta| order | 28980 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic7245 |
| unambiguous semidirect product | C7⋊Dic1035 |
| unambiguous semidirect product | C9⋊Dic805 |
| unambiguous semidirect product | C23⋊Dic315 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D7245 |
| commutator, hypocenter | C5×C7×C9×C23 | C4 |
| Frattini | C2×C3 | D2415 |
| Fitting, cosocle | C2×C5×C7×C9×C23 | C2 |
| socle, prime radical | C2×C3×C5×C7×C23 | D3 |
| LCS | G ▷ C5×C7×C9×C23 | |
| UCS | C1 ◁ C2 | |
72 conjugacy classes of subgroups.
| minimal degree | μ(G) = 48 |
| transitive degree | μt(G) = 28980 |
A minimal faithful permutation representation — 2 generators on 48 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)(26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,18)(16,17)(20,25)(21,24)(22,23)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)Polycyclic presentation:
2,3,5,7,23,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^4,d^a=d^6,e^a=e^22,g^a=g^27248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic14490 |
| maximal normal subgroup of | Dic14490 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28980, 17);