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C₁₃×C₄₁×C₇⋊C₉ #46777137

order	33579
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₄₁×C₇⋊C₉
unambiguous semidirect product	C₇⋊(C₉×C₁₃×C₄₁)
unambiguous semidirect product	(C₇×C₄₁)⋊(C₉×C₁₃)

Splittings

derived, Sylow	C₇ ⋊ C₉×C₁₃×C₄₁
Hall	C₇×C₁₃×C₄₁ ⋊ C₉
Hall	C₇×C₄₁ ⋊ C₉×C₁₃
Hall	C₇×C₁₃ ⋊ C₉×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₄₁	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₁₃×C₄₁
Frattini	C₃	C₁₃×ΓL(1,𝔽₈)×C₄₁
Fitting, socle, prime radical	C₃×C₇×C₁₃×C₄₁	C₃
cosocle	C₃×C₇	C₃×C₁₃×C₄₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃×C₄₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33579

Conjugacy classes & character table

7995 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33579, 3);