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D₅×D₁₆ #65199

order	320
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

D₅×D₁₆

Splittings

Fitting	C₅×D₁₆ ⋊ C₂
Sylow	C₅ ⋊ C₂×D₁₆

Subgroups

	subgroup	G/H
center	C₂	D₅×D₈
commutator, cosocle	C₅×C₈	C₂³
Frattini	C₈	C₂²×D₅
Fitting	C₅×D₁₆	C₂
socle	C₂×C₅	C₂×D₈
hypercenter	D₁₆	D₅
hypocenter	C₅	C₂×D₁₆
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ D₁₆

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 80

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

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

Conjugacy classes & character table

44 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598678, #10598681, D₅×D₃₂, …
maximal normal subgroup of	#10598678, #10598681, D₅×D₃₂, …
maximal quotient of	#10599967, #10599971, #10599976, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 537);