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C₂×C₁₁⋊C₁₆ #66875

order	352
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₁⋊C₁₆
unambiguous semidirect product	(C₂×C₁₁)⋊C₁₆

Splittings

C₁₁ ⋊ C₂×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₈	D₁₁
commutator, hypocenter	C₁₁	C₂×C₁₆
Frattini	C₈	C₂×D₁₁
Fitting	C₂×C₈×C₁₁	C₂
socle, prime radical	C₂²×C₁₁	C₈
cosocle	C₈×C₁₁	C₂²
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₈

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15,16,19,17,20,22,25,18,21,23,26,24,27,28,29);(1,2)(3,4,6,8,10,12,13,11,9,7,5)

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₁₁⋊C₁₆, #10622099, C₄⋊(C₁₁⋊C₁₆), …
maximal normal subgroup of	C₄×C₁₁⋊C₁₆, #10622099, C₄⋊(C₁₁⋊C₁₆), …
maximal quotient of	C₄×C₁₁⋊C₁₆, C₄⋊(C₁₁⋊C₁₆), C₂×C₁₁⋊C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(352, 17);