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D₈×D₁₁ #66963

order	352
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₈×D₁₁

Splittings

Fitting	C₁₁×D₈ ⋊ C₂
Sylow	C₁₁ ⋊ C₂×D₈

Subgroups

	subgroup	G/H
center	C₂	D₄×D₁₁
commutator, cosocle	C₄×C₁₁	C₂³
Frattini	C₄	C₂²×D₁₁
Fitting	C₁₁×D₈	C₂
socle	C₂×C₁₁	C₂×D₄
hypercenter	D₈	D₁₁
hypocenter	C₁₁	C₂×D₈
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 88

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

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

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₁×D₁₆, #10622524, D₁₁×SD₃₂, …
maximal normal subgroup of	D₁₁×D₁₆, #10622524, D₁₁×SD₃₂, …
maximal quotient of	#10622369, #10622372, #10622373, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 105);