Finite Group Databasebeta

← Prev (#91793) Next (#91795) →

C₂×Dic₆₀ #91794

order	480
isoclinism	isoclinic class of #6706
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

C₂×Dic₆₀

Splittings

Hall	C₃×C₅ ⋊ C₂×Q₁₆
Sylow	C₅ ⋊ C₂×Dic₁₂
Sylow	C₃ ⋊ C₂×Dic₂₀

Subgroups

	subgroup	G/H
center	C₂²	D₆₀
commutator, cosocle	C₃×C₄×C₅	C₂³
Frattini	C₄	C₂²×D₁₅
Fitting	C₂×C₃×C₅×C₈	C₂
socle, prime radical	C₂²×C₃×C₅	D₄
hypercenter	C₂×C₈	D₁₅
hypocenter	C₃×C₅	C₂×Q₁₆
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 480

A minimal faithful permutation representation — 3 generators on 26 points:

(3,4,5)(6,7,9,10,8)(11,13,20,24,15,22,14,21)(12,16,23,26,18,25,17,19);(1,2)(4,5)(7,8)(9,10)(11,12,15,18)(13,19,22,26)(14,23,20,17)(16,24,25,21);(1,2)

Conjugacy classes & character table

126 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11745901, #11745902, #11745925, …
maximal normal subgroup of	#11745901, #11745902, #11745925, …
maximal quotient of	#11750782, #11750783, C₄×Dic₆₀, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 870);