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C₂×#3959 #65437

order	320
isoclinism	isoclinic class of #3958
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Splittings

C₅ ⋊ C₂×SD₃₂

Subgroups

	subgroup	G/H
center	C₂²	#686
commutator, cosocle	C₅×C₈	C₂³
Frattini	C₈	C₂²×D₅
Fitting, prime radical	C₂×C₅×D₈	C₂
socle	C₂²×C₅	D₈
hypercenter	C₂×D₈	D₅
hypocenter	C₅	C₂×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

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

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10599968, #10599969, #10599986, …
maximal normal subgroup of	#10599968, #10599969, #10599986, …
maximal quotient of	C₂×#64710, C₂×#64712, #10601395, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 775);