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C₁₉×C₂²⋊(C₅²⋊C₉) #30685616

order	17100
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₁₉×C₂²⋊(C₅²⋊C₉)
unambiguous semidirect product	C₂²⋊(C₁₉×C₅²⋊C₉)
unambiguous semidirect product	C₅²⋊(C₁₉×C₂²⋊C₉)

Splittings

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

Subgroups

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

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1710

Conjugacy classes & character table

2052 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 253);