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C₂×D₄×D₁₁ #67035

order	352
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₄×D₁₁

Splittings

Fitting	C₂×D₄×C₁₁ ⋊ C₂
Sylow	C₁₁ ⋊ C₂²×D₄

Subgroups

	subgroup	G/H
center	C₂²	C₂²×D₁₁
commutator, cosocle	C₂×C₁₁	C₂⁴
Frattini	C₂	C₂³×D₁₁
Fitting	C₂×D₄×C₁₁	C₂
socle	C₂²×C₁₁	C₂³
hypercenter	C₂×D₄	D₁₁
hypocenter	C₁₁	C₂²×D₄
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×D₄

236 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 88

A minimal faithful permutation representation — 4 generators on 17 points:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₁×#99, D₁₁×#100, D₁₁×#102, …
maximal normal subgroup of	D₁₁×#99, D₁₁×#100, D₁₁×#102, …
maximal quotient of	C₂×#66931, C₂×C₂²⋊C₄×D₁₁, C₂×(C₂²⋊D₁₁)⋊C₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 177);