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C₄×D₅₂ #88127

order	416
isoclinism	isoclinic class of Dic₂₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

C₄×D₅₂

Splittings

Fitting	C₄²×C₁₃ ⋊ C₂
Sylow	C₁₃ ⋊ C₄×D₄

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂×D₁₃
commutator	C₂×C₁₃	C₂²×C₄
Frattini	C₂²	C₂²×D₁₃
Fitting	C₄²×C₁₃	C₂
socle, cosocle	C₂²×C₁₃	C₂³
prime radical	C₂×D₅₂	C₂
hypercenter	C₄²	D₁₃
hypocenter	C₁₃	C₄×D₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

94 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 21 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11718051, #11718075, C₈×D₅₂, …
maximal normal subgroup of	#11718051, #11718075, C₈×D₅₂, …
maximal quotient of	#11718314, #11718326, #11718329, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 94);