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C₂×#6092 #88105

order	416
isoclinism	isoclinic class of #261
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆ · Schur multiplier (H₂) = C₂

Aliases

Splittings

C₁₃ ⋊ C₂×C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	#261
commutator, hypocenter	C₁₃	C₂×C₁₆
Frattini	C₄	C₂×#261
Fitting	C₂×C₄×C₁₃	C₄
socle, prime radical	C₂²×C₁₃	C₈
cosocle	#1055	C₂²
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₄

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 2 generators on 31 points:

(4,5,6,8)(7,10,11,15)(9,13,14,12)(16,17,18,21,19,22,24,27,20,23,25,28,26,29,30,31);(1,2)(3,4,7,10,14,8,12,13,5,9,15,11,6)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×#6092, C₄⋊#6092, #11718231, …
maximal normal subgroup of	C₄×#6092, C₄⋊#6092, #11718231, …
maximal quotient of	C₄×#6092, C₄⋊#6092, C₂×#88036, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 72);