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D₇⋊C₉×C₂₈₉ #49138708

order	36414
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₂₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₂₈₉
unambiguous semidirect product	D₇⋊(C₉×C₂₈₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₂₈₉)
unambiguous semidirect product	(D₇×C₂₈₉)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₂₈₉
Hall	C₇⋊C₉×C₂₈₉ ⋊ C₂
Hall	D₇×C₂₈₉ ⋊ C₉
Hall	C₇×C₂₈₉ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₂₈₉
Hall	D₇ ⋊ C₉×C₂₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₂₈₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₂₈₉
Frattini	C₃×C₁₇	C₁₇×AGL(1,𝔽₇)
Fitting	C₃×C₇×C₂₈₉	C₂×C₃
socle, cosocle	C₃×C₇×C₁₇	C₂×C₃×C₁₇
prime radical	C₃×D₇×C₁₇	C₃×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₂₈₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18207

Conjugacy classes & character table

6069 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36414, 3);