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C₂×#3960 #65467

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

Aliases

Splittings

Fitting	C₂×C₅×Q₁₆ ⋊ C₂
Sylow	C₅ ⋊ C₂×SD₃₂

Subgroups

	subgroup	G/H
center	C₂²	#686
commutator, cosocle	C₅×C₈	C₂³
Frattini	C₈	C₂²×D₅
Fitting	C₂×C₅×Q₁₆	C₂
socle	C₂²×C₅	D₈
prime radical	C₂×D₄₀	C₂
hypercenter	C₂×Q₁₆	D₅
hypocenter	C₅	C₂×SD₃₂
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

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

Conjugacy classes & character table

50 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10599999, #10600001, #10600016, …
maximal normal subgroup of	#10599999, #10600001, #10600016, …
maximal quotient of	C₂×#64710, C₂×#64711, #10601393, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 805);