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C₂×C₈×D₁₁ #66952

order	352
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₈×D₁₁

Splittings

Fitting	C₂×C₈×C₁₁ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂²×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	D₁₁
commutator, hypocenter	C₁₁	C₂²×C₈
Frattini	C₄	C₂²×D₁₁
Fitting	C₂×C₈×C₁₁	C₂
socle	C₂²×C₁₁	C₂×C₄
prime radical	C₂²×D₁₁	C₄
cosocle	C₄×C₁₁	C₂³
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₈

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 176

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(C₂×D₁₁)⋊C₁₆, C₄×C₈×D₁₁, C₈×D₄₄, …
maximal normal subgroup of	(C₂×D₁₁)⋊C₁₆, C₄×C₈×D₁₁, C₈×D₄₄, …
maximal quotient of	C₈×Dic₂₂, C₄×C₈×D₁₁, #10622298, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 94);