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C₅×C₁₇⋊(D₇⋊C₉) #24924205

order	10710
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₇⋊(D₇⋊C₉)
unambiguous semidirect product	C₁₇⋊(C₅×D₇⋊C₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₅×D₁₇)
unambiguous semidirect product	D₁₁₉⋊(C₅×C₉)
unambiguous semidirect product	(C₅×D₁₁₉)⋊C₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅	C₁₇⋊AGL(1,𝔽₇)
commutator, hypocenter	C₇×C₁₇	C₂×C₅×C₉
Frattini	C₃	C₅×C₁₇⋊AGL(1,𝔽₇)
Fitting, socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₅×D₁₁₉	C₃
cosocle	C₃×C₇×C₁₇	C₂×C₃×C₅
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₃×C₅

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

705 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₅×D₁₇×D₇⋊C₉, D₅×C₁₇⋊(D₇⋊C₉), D₈₅⋊(D₇⋊C₉), …
maximal normal subgroup of	C₅×D₁₇×D₇⋊C₉, D₅×C₁₇⋊(D₇⋊C₉), D₈₅⋊(D₇⋊C₉), …
maximal quotient of	C₅×(C₇⋊C₉)⋊Dic₁₇, C₂×C₅×C₁₇⋊(D₇⋊C₉)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 20);