Finite Group Databasebeta

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C₉×C₁₇×D₃₅ #24924193

order	10710
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₇×D₃₅
unambiguous semidirect product	C₅⋊(C₉×D₇×C₁₇)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₇	D₃₅
commutator, hypocenter	C₅×C₇	C₂×C₉×C₁₇
Frattini	C₃	C₃×C₁₇×D₃₅
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₁₇×D₃₅	C₃
cosocle	C₃×C₅×C₇	C₂×C₃×C₁₇
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₉×C₁₇

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2907 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₇×D₃₅, C₉×D₅×D₇×C₁₇, C₉×D₃₅⋊D₁₇, …
maximal normal subgroup of	C₉×D₁₇×D₃₅, C₉×D₅×D₇×C₁₇, C₉×D₃₅⋊D₁₇, …
maximal quotient of	C₉×C₁₇×Dic₃₅, C₂×C₉×C₁₇×D₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 8);