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D₇⋊C₉×C₁₆₇ #35230910

order	21042
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₁₆₇
unambiguous semidirect product	D₇⋊(C₉×C₁₆₇)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₁₆₇)
unambiguous semidirect product	(D₇×C₁₆₇)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₆₇
Hall	C₇⋊C₉×C₁₆₇ ⋊ C₂
Hall	D₇×C₁₆₇ ⋊ C₉
Hall	C₇×C₁₆₇ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₁₆₇
Hall	D₇ ⋊ C₉×C₁₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₆₇	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₁₆₇
Frattini	C₃	AGL(1,𝔽₇)×C₁₆₇
Fitting, socle	C₃×C₇×C₁₆₇	C₂×C₃
prime radical	C₃×D₇×C₁₆₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₆₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 10521

Conjugacy classes & character table

3507 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21042, 11);