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C₅×C₁₇×D₇⋊C₉ #24924204

order	10710
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₇×D₇⋊C₉
unambiguous semidirect product	D₇⋊(C₅×C₉×C₁₇)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₅×C₁₇)
unambiguous semidirect product	(C₅×D₇)⋊(C₉×C₁₇)
unambiguous semidirect product	(D₇×C₁₇)⋊(C₅×C₉)
unambiguous semidirect product	(C₅×D₇×C₁₇)⋊C₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₅×C₁₇	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₅×C₉×C₁₇
Frattini	C₃	C₅×C₁₇×AGL(1,𝔽₇)
Fitting, socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₅×D₇×C₁₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₅×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₅×C₁₇

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₁₇×D₇⋊C₉, D₅×C₁₇×D₇⋊C₉, D₇⋊C₉×D₈₅, …
maximal normal subgroup of	C₅×D₁₇×D₇⋊C₉, D₅×C₁₇×D₇⋊C₉, D₇⋊C₉×D₈₅, …
maximal quotient of	C₅×C₁₇×Dic₇⋊C₉, C₂×C₅×C₁₇×D₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 19);