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C₅²×Dic₁₇₁ #30685451

order	17100
automorphism	?
homology	Abelianization (H₁) = C₄×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×Dic₁₇₁
unambiguous semidirect product	C₉⋊(C₅²×Dic₁₉)
unambiguous semidirect product	C₁₉⋊(C₅²×Dic₉)

Splittings

derived, Hall	C₉×C₁₉ ⋊ C₄×C₅²
Hall	C₅²×C₉×C₁₉ ⋊ C₄
Hall	C₅²×C₁₉ ⋊ Dic₉
Hall	C₅²×C₉ ⋊ Dic₁₉
Sylow	C₁₉ ⋊ C₅²×Dic₉
Sylow	C₉ ⋊ C₅²×Dic₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅²	D₁₇₁
commutator, hypocenter	C₉×C₁₉	C₄×C₅²
Frattini	C₂×C₃	C₅²×D₅₇
Fitting	C₂×C₅²×C₉×C₁₉	C₂
socle, prime radical	C₂×C₃×C₅²×C₁₉	D₃
cosocle	C₂×C₉×C₁₉	C₂×C₅²
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂×C₅²

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17100

Conjugacy classes & character table

4350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17100, 88);