Finite Group Databasebeta

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C₂²×C₅²×#4294 #30685611

order	17100
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₅²×#4294

Splittings

derived, Sylow	C₁₉ ⋊ C₂²×C₅²×C₉
Hall	C₂²×C₅²×C₁₉ ⋊ C₉
Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₂²×C₁₉ ⋊ C₅²×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂²×C₃×C₅²	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₂²×C₅²×C₉
Frattini	C₃	C₂²×C₅²×C₁₉⋊C₃
Fitting, socle, prime radical	C₂²×C₃×C₅²×C₁₉	C₃
cosocle	C₃×C₁₉	C₂²×C₃×C₅²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂²×C₃×C₅²

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17100

Conjugacy classes & character table

2700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 248);