Finite Group Databasebeta

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C₃²×C₅×C₁₉×Dic₅ #30685679

order	17100
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

C₃²×C₅×C₁₉×Dic₅

Splittings

derived	C₅ ⋊ C₃²×C₄×C₅×C₁₉
Hall	C₃²×C₅²×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ C₃²×C₄
Hall	C₃²×C₅² ⋊ C₄×C₁₉
Sylow	C₅² ⋊ C₃²×C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₅×C₁₉	D₅
commutator, hypocenter	C₅	C₃²×C₄×C₅×C₁₉
Frattini	C₂	C₃²×C₅×D₅×C₁₉
Fitting, socle, prime radical	C₂×C₃²×C₅²×C₁₉	C₂
cosocle	C₂×C₅	C₂×C₃²×C₅×C₁₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₃²×C₅×C₁₉

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

6840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 316);