Dic₁₀₁ #87936

order	404
isoclinism	isoclinic class of D₁₀₁
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic

Dic₁₀₁

Splittings

derived, Sylow

C₁₀₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₀₁
commutator, hypocenter	C₁₀₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₀₁	C₂
LCS	G ▷ C₁₀₁
UCS	C₁ ◁ C₂

6 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 404

A minimal faithful permutation representation — 2 generators on 105 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(1,3,2,4)(6,105)(7,104)(8,103)(9,102)(10,101)(11,100)(12,99)(13,98)(14,97)(15,96)(16,95)(17,94)(18,93)(19,92)(20,91)(21,90)(22,89)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)

Polycyclic presentation:

2^2,101|a^2=b,c^a=c^100

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11717581, Dic₂₀₂, C₄×D₁₀₁, …
maximal normal subgroup of	#11717581, Dic₂₀₂, C₄×D₁₀₁, …
maximal quotient of	#11717579, C₂×Dic₁₀₁, C₃×Dic₁₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(404, 1);

Dic101 #87936