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D₁₇×C₄₉⋊C₉ #28418310

order	14994
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₇×C₄₉⋊C₉
unambiguous semidirect product	C₁₇⋊(C₂×C₄₉⋊C₉)
unambiguous semidirect product	(D₁₇×C₄₉)⋊C₉

Splittings

derived, Hall	C₁₇×C₄₉ ⋊ C₂×C₉
Hall	C₁₇×C₄₉⋊C₉ ⋊ C₂
Hall	D₁₇×C₄₉ ⋊ C₉
Sylow	C₄₉ ⋊ C₉×D₁₇
Sylow	C₁₇ ⋊ C₂×C₄₉⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₁₇×C₄₉⋊C₃
commutator, hypocenter	C₁₇×C₄₉	C₂×C₉
Frattini	C₃×C₇	ΓL(1,𝔽₈)×D₁₇
Fitting, cosocle	C₃×C₁₇×C₄₉	C₂×C₃
socle	C₃×C₇×C₁₇	C₂×ΓL(1,𝔽₈)
prime radical	C₃×C₇×D₁₇	ΓL(1,𝔽₈)
LCS	G ▷ C₁₇×C₄₉
UCS	C₁ ◁ C₃

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7497

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#595×C₄₉⋊C₉, (C₄₉⋊C₉)⋊#595, D₁₇×D₄₉⋊C₉, …
maximal normal subgroup of	#595×C₄₉⋊C₉, (C₄₉⋊C₉)⋊#595, D₁₇×D₄₉⋊C₉, …
maximal quotient of	Dic₁₇×C₄₉⋊C₉, C₂×D₁₇×C₄₉⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14994, 2);