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D₇×C₁₇×C₁₃⋊C₃ #22604657

order	9282
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

D₇×C₁₇×C₁₃⋊C₃

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇	D₇×C₁₃⋊C₃
commutator, hypocenter	C₇×C₁₃	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₁₇

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

595 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×C₁₇×D₁₃⋊C₃, D₇×C₁₇⋊(D₁₃⋊C₃), D₇×D₁₇×C₁₃⋊C₃, …
maximal normal subgroup of	D₇×C₁₇×D₁₃⋊C₃, D₇×C₁₇⋊(D₁₃⋊C₃), D₇×D₁₇×C₁₃⋊C₃, …
maximal quotient of	C₁₇×Dic₇×C₁₃⋊C₃, C₂×D₇×C₁₇×C₁₃⋊C₃, D₇×C₁₇×C₁₃⋊C₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9282, 33);