Dic₁₁₇ #90830

order	468
isoclinism	isoclinic class of D₁₁₇
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₁₁₇
unambiguous semidirect product	C₉⋊Dic₁₃

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 468

A minimal faithful permutation representation — 2 generators on 26 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)

Polycyclic presentation:

2^2,3,13,3|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^12,e^a=e^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 5);