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SD₁₆×D₁₁ #66966

order	352
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

SD₁₆×D₁₁

Splittings

Fitting	C₁₁×SD₁₆ ⋊ C₂
Sylow	C₁₁ ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂	D₄×D₁₁
commutator, cosocle	C₄×C₁₁	C₂³
Frattini	C₄	C₂²×D₁₁
Fitting	C₁₁×SD₁₆	C₂
socle	C₂×C₁₁	C₂×D₄
prime radical	D₄×D₁₁	C₂
hypercenter	SD₁₆	D₁₁
hypocenter	C₁₁	C₂×SD₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

68 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);(12,13,15,18)(14,16,19,17)

Conjugacy classes & character table

49 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×SD₁₆×D₁₁, #10623293, D₁₁×#135, …
maximal normal subgroup of	C₂×SD₁₆×D₁₁, #10623293, D₁₁×#135, …
maximal quotient of	#10622371, #10622373, #10622374, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 108);