Finite Group Databasebeta

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C₇×C₄₁⋊(D₇⋊C₉) #49116293

order	36162
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₄₁⋊(D₇⋊C₉)
unambiguous semidirect product	C₄₁⋊(C₇×D₇⋊C₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₇×D₄₁)
unambiguous semidirect product	D₂₈₇⋊(C₇×C₉)

Splittings

derived	C₇×C₄₁ ⋊ C₂×C₇×C₉
Hall	C₇×C₄₁×C₇⋊C₉ ⋊ C₂
Hall	C₇×D₂₈₇ ⋊ C₉
Hall	C₇²×C₄₁ ⋊ C₂×C₉
Hall	C₇×C₇⋊C₉ ⋊ D₄₁
Sylow	C₇² ⋊ C₉×D₄₁
Sylow	C₄₁ ⋊ C₇×D₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	ΓL(1,𝔽₈)⋊D₄₁
commutator, hypocenter	C₇×C₄₁	C₂×C₇×C₉
Frattini	C₃	C₇×ΓL(1,𝔽₈)⋊D₄₁
Fitting, socle	C₃×C₇²×C₄₁	C₂×C₃
prime radical	C₃×C₇×D₂₈₇	C₃
cosocle	C₃×C₇×C₄₁	C₂×C₃×C₇
LCS	G ▷ C₇×C₄₁
UCS	C₁ ◁ C₃×C₇

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5166

Conjugacy classes & character table

2247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36162, 35);