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C₂×(C₅⋊D₅)⋊#4296 #30685729

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

Aliases

direct product	C₂×(C₅⋊D₅)⋊#4296
unambiguous semidirect product	(C₂×C₅⋊D₅)⋊#4296

Splittings

Fitting, socle	C₂×C₅²×C₁₉ ⋊ C₂×C₉
derived, Hall	C₅²×C₁₉ ⋊ C₂²×C₉
Hall	C₅²⋊#4296 ⋊ C₂²
Hall	C₂×C₁₉×C₅⋊D₅ ⋊ C₉
Hall	C₂×C₅⋊D₅ ⋊ #4296
Sylow	C₅² ⋊ C₂²×#4296
Sylow	C₁₉ ⋊ C₂×(C₅⋊D₅)⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	(C₅⋊D₅)⋊#4296
commutator, hypocenter	C₅²×C₁₉	C₂²×C₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₉	C₂×C₉
prime radical	C₂×C₅⋊D₅×C₁₉⋊C₃	C₃
cosocle	C₅²×C₁₉⋊C₃	C₂²×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₂

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 570

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 366);