Finite Group Databasebeta

← Prev (#65190) Next (#65192) →

C₂×D₈₀ #65191

order	320
isoclinism	isoclinic class of D₈₀
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂³

Aliases

C₂×D₈₀

Splittings

Fitting	C₂×C₅×C₁₆ ⋊ C₂
Sylow	C₅ ⋊ C₂×D₁₆

Subgroups

	subgroup	G/H
center	C₂²	D₄₀
commutator, cosocle	C₅×C₈	C₂³
Frattini	C₈	C₂²×D₅
Fitting	C₂×C₅×C₁₆	C₂
socle	C₂²×C₅	D₈
hypercenter	C₂×C₁₆	D₅
hypocenter	C₅	C₂×D₁₆
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 160

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10598068, #10598074, #10598087, …
maximal normal subgroup of	#10598068, #10598074, #10598087, …
maximal quotient of	#10599837, C₄×D₈₀, #10599851, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 529);