Finite Group Databasebeta

← Prev (#66073) Next (#66075) →

C₂²×D₄₀ #66074

order	320
isoclinism	isoclinic class of #677
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂²×D₄₀

Splittings

Fitting	C₂²×C₅×C₈ ⋊ C₂
Sylow	C₅ ⋊ C₂²×D₈

Subgroups

	subgroup	G/H
center	C₂³	D₂₀
commutator, cosocle	C₄×C₅	C₂⁴
Frattini	C₄	C₂³×D₅
Fitting	C₂²×C₅×C₈	C₂
socle	C₂³×C₅	D₄
hypercenter	C₂²×C₈	D₅
hypocenter	C₅	C₂²×D₈
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 160

A minimal faithful permutation representation — 4 generators on 17 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#10599466, #10599467, #10599468, …
maximal normal subgroup of	#10599466, #10599467, #10599468, …
maximal quotient of	C₂×#64971, C₂×C₄×D₄₀, C₂×#64983, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(320, 1412);