Dic₁₁₆ #90775

order	464
isoclinism	isoclinic class of #90773
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

dicyclic

Dic₁₁₆

Splittings

Sylow

C₂₉ ⋊ Q₁₆

Subgroups

	subgroup	G/H
center	C₂	D₁₁₆
commutator, cosocle	C₄×C₂₉	C₂²
Frattini	C₄	C₂×D₂₉
Fitting	C₈×C₂₉	C₂
socle, prime radical	C₂×C₂₉	D₄
hypercenter	C₈	D₂₉
hypocenter	C₂₉	Q₁₆
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 464

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2,3,4,5,6,7,8)(9,16,15,14,13,12,11,10)(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);(1,9,5,13)(2,10,6,14)(3,11,7,15)(4,12,8,16)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Polycyclic presentation:

2^4,29|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,e^a=e^28

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745148, Dic₂₃₂, #11745175, …
maximal normal subgroup of	#11745148, Dic₂₃₂, #11745175, …
maximal quotient of	#11745164, #11745166, C₂×Dic₁₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 8);

Dic116 #90775