Finite Group Databasebeta

← Prev (#66920) Next (#66922) →

C₄×Dic₂₂ #66921

order	352
isoclinism	isoclinic class of Dic₂₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Dic₂₂

Splittings

C₁₁ ⋊ C₄×Q₈

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₄
Frattini	C₂²	C₂²×D₁₁
Fitting	C₄²×C₁₁	C₂
socle, prime radical, cosocle	C₂²×C₁₁	C₂³
hypercenter	C₄²	D₁₁
hypocenter	C₁₁	C₄×Q₈
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

70 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 3 generators on 23 points:

(1,2,4,6,8,10,11,9,7,5,3)(16,18,19,23)(17,20,21,22);(2,3)(4,5)(6,7)(8,9)(10,11)(16,17,19,21)(18,22,23,20);(12,13,14,15)

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10622094, #10622122, C₈×Dic₂₂, …
maximal normal subgroup of	#10622094, #10622122, C₈×Dic₂₂, …
maximal quotient of	#10622259, #10622260, #10622267, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 63);