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C₂×#3932 #65192

order	320
isoclinism	isoclinic class of D₈₀
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

Fitting	C₂×C₅×C₁₆ ⋊ C₂
Sylow	C₅ ⋊ C₂×SD₃₂

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
prime radical	C₂×D₄₀	C₂
hypercenter	C₂×C₁₆	D₅
hypocenter	C₅	C₂×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

90 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)(8,9,14,20,19,23,10,13,12,16,17,22,11,15,18,21);(1,2)(4,5)(6,7)(9,13)(10,17)(11,19)(14,18)(15,22)(16,21)(20,23);(1,2)

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10599854, #10599855, C₄×#3932, …
maximal normal subgroup of	#10599854, #10599855, C₄×#3932, …
maximal quotient of	#10599839, #10599851, #10599854, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 530);