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C₉×D₁₂₇⋊C₇ #30630658

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

Aliases

direct product	C₉×D₁₂₇⋊C₇
unambiguous semidirect product	(C₉×D₁₂₇)⋊C₇

Splittings

Fitting, Hall	C₉×C₁₂₇ ⋊ C₂×C₇
derived, Sylow	C₁₂₇ ⋊ C₂×C₇×C₉
Hall	C₉×C₁₂₇⋊C₇ ⋊ C₂
Hall	C₉×D₁₂₇ ⋊ C₇
Hall	C₁₂₇⋊C₇ ⋊ C₂×C₉
Hall	D₁₂₇ ⋊ C₇×C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₂₇⋊C₇
commutator, hypocenter	C₁₂₇	C₂×C₇×C₉
Frattini	C₃	C₃×D₁₂₇⋊C₇
Fitting	C₉×C₁₂₇	C₂×C₇
socle, cosocle	C₃×C₁₂₇	C₂×C₃×C₇
prime radical	C₃×D₁₂₇⋊C₇	C₃
LCS	G ▷ C₁₂₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×D₁₂₇⋊C₇, C₂×C₉×D₁₂₇⋊C₇
maximal normal subgroup of	D₉×D₁₂₇⋊C₇, C₂×C₉×D₁₂₇⋊C₇
maximal quotient of	C₉×Dic₁₂₇⋊C₇, C₂×C₉×D₁₂₇⋊C₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 15);