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C₂×C₇⋊C₉×C₁₂₇ #30630647

order	16002
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇⋊C₉×C₁₂₇
unambiguous semidirect product	(C₂×C₇)⋊(C₉×C₁₂₇)

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₂₇
Hall	C₂×C₇×C₁₂₇ ⋊ C₉
Hall	C₇×C₁₂₇ ⋊ C₂×C₉
Hall	C₂×C₇ ⋊ C₉×C₁₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₂₇	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₁₂₇
Frattini	C₃	C₂×ΓL(1,𝔽₈)×C₁₂₇
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₂₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₂₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₂₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3810 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇⋊C₉×C₁₂₇, C₇⋊C₉×Dic₁₂₇, C₁₂₇×Dic₇⋊C₉, …
maximal normal subgroup of	C₄×C₇⋊C₉×C₁₂₇, C₇⋊C₉×Dic₁₂₇, C₁₂₇×Dic₇⋊C₉, …
maximal quotient of	C₄×C₇⋊C₉×C₁₂₇, C₂²×C₇⋊C₉×C₁₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 4);