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C₇×C₉×D₁₂₇ #30630651

order	16002
isoclinism	isoclinic class of D₁₂₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₇×C₉×D₁₂₇

Splittings

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

Subgroups

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

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4095 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₂₇, C₇×D₉×D₁₂₇, D₆₃×D₁₂₇, …
maximal normal subgroup of	C₉×D₇×D₁₂₇, C₇×D₉×D₁₂₇, D₆₃×D₁₂₇, …
maximal quotient of	C₇×C₉×Dic₁₂₇, C₂×C₇×C₉×D₁₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 8);