Finite Group Databasebeta

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C₅×C₉×Dic₉₅ #30685447

order	17100
isoclinism	isoclinic class of D₉₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₉×Dic₉₅

Splittings

derived	C₅×C₁₉ ⋊ C₄×C₅×C₉
Hall	C₅²×C₉×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ C₄×C₉
Hall	C₅²×C₉ ⋊ Dic₁₉
Hall	C₉×C₁₉ ⋊ C₅×Dic₅
Sylow	C₅² ⋊ C₉×Dic₁₉
Sylow	C₁₉ ⋊ C₅×C₉×Dic₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₉	D₉₅
commutator, hypocenter	C₅×C₁₉	C₄×C₅×C₉
Frattini	C₂×C₃	C₃×C₅×D₉₅
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₅²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₅×C₁₉	C₂×C₃×C₅
LCS	G ▷ C₅×C₁₉
UCS	C₁ ◁ C₂×C₅×C₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 3420

Conjugacy classes & character table

4410 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 84);