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D₇×C₄₁×C₇⋊C₉ #49116307

order	36162
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

D₇×C₄₁×C₇⋊C₉

Splittings

derived, Sylow	C₇² ⋊ C₂×C₉×C₄₁
Hall	C₇×C₄₁×C₇⋊C₉ ⋊ C₂
Hall	C₇×D₇×C₄₁ ⋊ C₉
Hall	C₇²×C₄₁ ⋊ C₂×C₉
Hall	C₇×C₇⋊C₉ ⋊ C₂×C₄₁
Hall	C₇×D₇ ⋊ C₉×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₁	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₂×C₉×C₄₁
Frattini	C₃	D₇×ΓL(1,𝔽₈)×C₄₁
Fitting, socle	C₃×C₇²×C₄₁	C₂×C₃
prime radical	C₃×C₇×D₇×C₄₁	C₃
cosocle	C₃×C₇²	C₂×C₃×C₄₁
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₄₁

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 5166

Conjugacy classes & character table

3075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36162, 49);