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C₄×D₄₄ #66926

order	352
isoclinism	isoclinic class of Dic₂₂
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₄×D₄₄

Splittings

Fitting	C₄²×C₁₁ ⋊ C₂
Sylow	C₁₁ ⋊ C₄×D₄

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₄
Frattini	C₂²	C₂²×D₁₁
Fitting	C₄²×C₁₁	C₂
socle, cosocle	C₂²×C₁₁	C₂³
prime radical	C₂×D₄₄	C₂
hypercenter	C₄²	D₁₁
hypocenter	C₁₁	C₄×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 3 generators on 19 points:

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

Conjugacy classes & character table

100 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10622097, #10622121, C₈×D₄₄, …
maximal normal subgroup of	#10622097, #10622121, C₈×D₄₄, …
maximal quotient of	#10622266, #10622278, #10622281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 68);