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D₇⋊C₉×C₁₂₇ #30630666

order	16002
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₂₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₁₂₇
unambiguous semidirect product	D₇⋊(C₉×C₁₂₇)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₁₂₇)

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₂₇
Hall	C₇⋊C₉×C₁₂₇ ⋊ C₂
Hall	D₇×C₁₂₇ ⋊ C₉
Hall	C₇×C₁₂₇ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₁₂₇
Hall	D₇ ⋊ C₉×C₁₂₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₂₇	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₁₂₇
Frattini	C₃	AGL(1,𝔽₇)×C₁₂₇
Fitting, socle	C₃×C₇×C₁₂₇	C₂×C₃
prime radical	C₃×D₇×C₁₂₇	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₂₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₂₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2667 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇⋊C₉×D₁₂₇, C₂×D₇⋊C₉×C₁₂₇
maximal normal subgroup of	D₇⋊C₉×D₁₂₇, C₂×D₇⋊C₉×C₁₂₇
maximal quotient of	C₁₂₇×Dic₇⋊C₉, C₂×D₇⋊C₉×C₁₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16002, 23);