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C₉×D₇×C₁₂₇ #30630652

order	16002
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₂₇ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₂₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₂₇	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₂₇
Frattini	C₃	C₃×D₇×C₁₂₇
Fitting	C₇×C₉×C₁₂₇	C₂
socle	C₃×C₇×C₁₂₇	C₂×C₃
prime radical	C₃×D₇×C₁₂₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₂₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₂₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5715 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₂₇, D₇×D₉×C₁₂₇, D₇×D₁₁₄₃, …
maximal normal subgroup of	C₉×D₇×D₁₂₇, D₇×D₉×C₁₂₇, D₇×D₁₁₄₃, …
maximal quotient of	C₉×Dic₇×C₁₂₇, C₂×C₉×D₇×C₁₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 9);