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M₁₆×D₁₁ #66959

order	352
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

M₁₆×D₁₁

Splittings

Fitting	C₁₁×M₁₆ ⋊ C₂
Sylow	C₁₁ ⋊ C₂×M₁₆

Subgroups

	subgroup	G/H
center, Frattini	C₄	C₂²×D₁₁
commutator, socle	C₂×C₁₁	C₂²×C₄
Fitting	C₁₁×M₁₆	C₂
prime radical	C₂²×D₁₁	C₄
cosocle	C₄×C₁₁	C₂³
hypercenter	M₁₆	D₁₁
hypocenter	C₁₁	C₂×M₁₆
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ M₁₆

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₁×#100, #10622358, D₁₁×#101, …
maximal normal subgroup of	D₁₁×#100, #10622358, D₁₁×#101, …
maximal quotient of	#10622314, D₁₁×#97, #10622318, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 101);