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C₂×#6118 #88233

order	416
isoclinism	isoclinic class of #6118
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

C₁₃ ⋊ C₂×M₁₆

Subgroups

	subgroup	G/H
center	C₂²	C₂×#261
commutator	C₂×C₁₃	C₂²×C₄
Frattini	C₂	C₂²×#261
Fitting	C₂×C₄×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄
prime radical	C₂²×D₁₃	C₄
cosocle	Dic₁₃	C₂³
hypercenter	C₂×C₄	#261
hypocenter	C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 23 points:

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11718247, #11718268, #11718274, …
maximal normal subgroup of	#11718247, #11718268, #11718274, …
maximal quotient of	C₄×#6118, #11719051, #11719052, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 200);