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C₂×C₅⋊D₅×#4294 #30685563

order	17100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×#4294
unambiguous semidirect product	(C₂×C₅)⋊(D₅×#4294)

Splittings

derived, Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²×#4294 ⋊ C₂²
Hall	C₂×C₁₉×C₅⋊D₅ ⋊ C₉
Sylow	C₅² ⋊ C₂²×#4294
Sylow	C₁₉ ⋊ C₂×C₉×C₅⋊D₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₅⋊D₅×C₁₉⋊C₃
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₃	C₂×C₅⋊D₅×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×C₅⋊D₅	C₃
cosocle	C₃×C₅²×C₁₉	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂×C₃

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8550

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 200);