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C₄×C₁₁⋊C₈ #66866

order	352
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₈ · Schur multiplier (H₂) = C₄

Aliases

C₄×C₁₁⋊C₈

Splittings

C₁₁ ⋊ C₄×C₈

Subgroups

	subgroup	G/H
center, hypercenter	C₄²	D₁₁
commutator, hypocenter	C₁₁	C₄×C₈
Frattini	C₂×C₄	C₂×D₁₁
Fitting	C₄²×C₁₁	C₂
socle, prime radical	C₂²×C₁₁	C₂×C₄
cosocle	C₂×C₄×C₁₁	C₂²
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₄²

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 2 generators on 23 points:

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

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₈×C₁₁⋊C₈, #10622092, #10622093, …
maximal normal subgroup of	C₈×C₁₁⋊C₈, #10622092, #10622093, …
maximal quotient of	C₈×C₁₁⋊C₈, #10622093, C₄×C₁₁⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 8);