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C₂×C₉×C₁₂₇⋊C₇ #30630645

order	16002
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

450 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×C₉×C₁₂₇⋊C₇, C₉×Dic₁₂₇⋊C₇, Dic₉×C₁₂₇⋊C₇, …
maximal normal subgroup of	C₄×C₉×C₁₂₇⋊C₇, C₉×Dic₁₂₇⋊C₇, Dic₉×C₁₂₇⋊C₇, …
maximal quotient of	C₄×C₉×C₁₂₇⋊C₇, C₂²×C₉×C₁₂₇⋊C₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 2);