Finite Group Databasebeta

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C₅×D₃×#170 #11925331

order	1200
isoclinism	isoclinic class of D₃×AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₈ · Schur multiplier (H₂) = C₂

Aliases

C₅×D₃×#170

Splittings

derived	C₃×C₅ ⋊ C₂×C₅×C₈
Hall	C₃×C₅² ⋊ C₂×C₈
Sylow	C₅² ⋊ D₃×C₈
Sylow	C₃ ⋊ C₂×C₅×#170

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅	D₃×AGL(1,𝔽₅)
commutator, hypocenter	C₃×C₅	C₂×C₅×C₈
Frattini	C₂	C₅×D₃×AGL(1,𝔽₅)
Fitting, socle	C₂×C₃×C₅²	C₂×C₄
prime radical	C₂×C₅²×D₃	C₄
cosocle	C₃×Dic₅	C₂²×C₅
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₅

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#87827, C₅×D₃×#704, D₃×#87829, …
maximal normal subgroup of	D₃×#87827, C₅×D₃×#704, D₃×#87829
maximal quotient of	C₅×#10623980

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 541);