Finite Group Databasebeta

← Prev (#91971) Next (#91973) →

C₂×C₃×#700 #91972

order	480
isoclinism	isoclinic class of #700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₂×C₃×#700

Splittings

Hall	C₃×C₅ ⋊ C₂×M₁₆
Sylow	C₅ ⋊ C₂×C₃×M₁₆

Subgroups

	subgroup	G/H
center	C₂²×C₃	C₂×AGL(1,𝔽₅)
commutator	C₂×C₅	C₂²×C₃×C₄
Frattini	C₂	C₂²×C₃×AGL(1,𝔽₅)
Fitting	C₂×C₃×C₄×C₅	C₄
socle	C₂²×C₃×C₅	C₂×C₄
prime radical	C₂²×C₃×D₅	C₄
cosocle	Dic₅	C₂³×C₃
hypercenter	C₂×C₃×C₄	AGL(1,𝔽₅)
hypocenter	C₅	C₂×C₃×M₁₆
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 240

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2)(3,4,5)(6,7,8,10,9)(11,13,15,14)(12,16,17,18);(7,8,9,10)(11,12,14,16,15,17,13,18);(1,2)

Conjugacy classes & character table

84 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11746524, #11746532, #11746536, …
maximal normal subgroup of	#11746524, #11746532, #11746536, …
maximal quotient of	C₃×C₄×#700, C₃×#65680, C₃×#65681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1048);