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C₂×#1039 #6048

order	200
isoclinism	isoclinic class of C₅⋊D₅
automorphism	Aut(G) order 96000
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂×C₅

Aliases

Splittings

C₅² ⋊ C₂×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	C₅⋊D₅
commutator, hypocenter	C₅²	C₂×C₄
Frattini	C₂	C₂×C₅⋊D₅
Fitting, socle, prime radical	C₂²×C₅²	C₂
cosocle	C₂×C₅²	C₂²
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 16
transitive degree	μ_t(G) = 200

A minimal faithful permutation representation — 3 generators on 16 points:

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

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

derived subgroup of	#13099965, #13099966, #13099967, …
maximal subgroup of	Dic₅², #87778, #87780, …
maximal normal subgroup of	Dic₅², #87778, #87780, …
maximal quotient of	C₂×#6029, #87804, C₄×#1039, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(200, 35);