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D₃×C₇×C₁₂₇⋊C₃ #30630716

order	16002
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₃×C₇×C₁₂₇⋊C₃
unambiguous semidirect product	C₃⋊(C₂×C₇×C₁₂₇⋊C₃)

Splittings

Fitting, socle	C₃×C₇×C₁₂₇ ⋊ C₂×C₃
derived	C₃×C₁₂₇ ⋊ C₂×C₃×C₇
Hall	C₃×C₇×C₁₂₇⋊C₃ ⋊ C₂
Hall	C₃×C₁₂₇⋊C₃ ⋊ C₂×C₇
Hall	C₇×C₁₂₇ ⋊ C₃×D₃
Sylow	C₁₂₇ ⋊ C₃×D₃×C₇

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₃×C₁₂₇⋊C₃
commutator, cosocle, hypocenter	C₃×C₁₂₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₂₇	C₂×C₃
LCS	G ▷ C₃×C₁₂₇
UCS	C₁ ◁ C₇

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

945 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×C₇×D₁₂₇⋊C₃, D₃×(C₁₂₇⋊C₃)⋊D₇, D₃×D₇×C₁₂₇⋊C₃, …
maximal normal subgroup of	D₃×C₇×D₁₂₇⋊C₃, D₃×(C₁₂₇⋊C₃)⋊D₇, D₃×D₇×C₁₂₇⋊C₃, …
maximal quotient of	C₇×Dic₃×C₁₂₇⋊C₃, C₂×D₃×C₇×C₁₂₇⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 73);