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C₂×C₃×Dic₃×AGL(1,𝔽₅) #13088645

order	1440
isoclinism	isoclinic class of D₃×AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

C₂×C₃×Dic₃×AGL(1,𝔽₅)

Splittings

derived	C₃×C₅ ⋊ C₂×C₃×C₄²
Hall	C₃²×C₅ ⋊ C₂×C₄²
Sylow	C₃² ⋊ C₂×C₄×AGL(1,𝔽₅)
Sylow	C₅ ⋊ C₂×C₃×C₄×Dic₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₂×C₃×C₄²
Frattini	C₂	C₂×C₃×D₃×AGL(1,𝔽₅)
Fitting, socle	C₂²×C₃²×C₅	C₂×C₄
prime radical	C₂²×C₃²×D₅	C₂²
cosocle	C₂×C₃×D₅	C₂³×C₃
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂²×C₃

486 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃×AGL(1,𝔽₅)×#67, C₂×AGL(1,𝔽₅)×#626, C₃×AGL(1,𝔽₅)×#237, …
maximal normal subgroup of	C₂×C₃×AGL(1,𝔽₅)×#67, C₂×AGL(1,𝔽₅)×#626, C₃×AGL(1,𝔽₅)×#237, …
maximal quotient of	C₃×AGL(1,𝔽₅)×#208, C₃×AGL(1,𝔽₅)×#217, C₂×C₃×ΓL(1,𝔽₁₆)⋊AGL(1,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4962);