Finite Group Databasebeta

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C₃×D₇×C₅⋊D₅ #14523637

order	2100
isoclinism	isoclinic class of D₇×C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₃×D₇×C₅⋊D₅

Splittings

Fitting, socle, Hall	C₃×C₅²×C₇ ⋊ C₂²
derived, Hall	C₅²×C₇ ⋊ C₂²×C₃
Hall	C₃×C₅² ⋊ C₂×D₇
Sylow	C₅² ⋊ C₂×C₃×D₇
Hall	C₃×C₇ ⋊ C₂×C₅⋊D₅
Sylow	C₇ ⋊ C₂×C₃×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₇×C₅⋊D₅
commutator, cosocle, hypocenter	C₅²×C₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇	C₂²
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₃

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 525

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₅⋊D₅×D₄₉, D₇×C₅⋊(C₅⋊AGL(1,𝔽₇)), (ΓL(1,𝔽₈)⋊D₇)⋊(C₅⋊D₅), …
maximal normal subgroup of	C₃×C₇×D₇×C₅⋊D₅, C₃×C₁₁×D₇×C₅⋊D₅, C₃×C₁₃×D₇×C₅⋊D₅, …
maximal quotient of	C₃×C₅⋊D₅×D₄₉, D₇×C₅⋊(C₅⋊AGL(1,𝔽₇)), (ΓL(1,𝔽₈)⋊D₇)⋊(C₅⋊D₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2100, 117);