Dic₉₁ #67242

order	364
isoclinism	isoclinic class of D₉₁
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₉₁
unambiguous semidirect product	C₇⋊Dic₁₃

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₉₁
commutator, hypocenter	C₇×C₁₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₇×C₁₃	C₂
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 364

A minimal faithful permutation representation — 2 generators on 24 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);(1,3,2,4)(6,11)(7,10)(8,9)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)

Polycyclic presentation:

2^2,7,13|a^2=b,c^a=c^6,d^a=d^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(364, 3);