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D₅×C₁₇×C₇⋊C₉ #24924206

order	10710
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₁₇×C₇⋊C₉
unambiguous semidirect product	C₅⋊(C₂×C₁₇×C₇⋊C₉)
unambiguous semidirect product	(C₇×D₅)⋊(C₉×C₁₇)
unambiguous semidirect product	(C₇×D₅×C₁₇)⋊C₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₅×ΓL(1,𝔽₈)
commutator, hypocenter	C₅×C₇	C₂×C₉×C₁₇
Frattini	C₃	D₅×C₁₇×ΓL(1,𝔽₈)
Fitting, socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₇×D₅×C₁₇	C₃
cosocle	C₃×C₅×C₇	C₂×C₃×C₁₇
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₃×C₁₇

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₇×(C₇⋊C₉)⋊AGL(1,𝔽₅), (C₇⋊C₉)⋊#66774, C₁₇×AGL(1,𝔽₅)×C₇⋊C₉, …
maximal normal subgroup of	C₁₇×(C₇⋊C₉)⋊AGL(1,𝔽₅), (C₇⋊C₉)⋊#66774, C₁₇×AGL(1,𝔽₅)×C₇⋊C₉, …
maximal quotient of	C₁₇×Dic₅×C₇⋊C₉, C₂×D₅×C₁₇×C₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 21);