Finite Group Databasebeta

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C₂×(C₇⋊C₉)⋊D₁₃₇ #46828575

order	34524
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₇⋊C₉)⋊D₁₃₇
unambiguous semidirect product	(C₂×C₇⋊C₉)⋊D₁₃₇
unambiguous semidirect product	(C₂×C₁₃₇)⋊(D₇⋊C₉)
unambiguous semidirect product	(C₂×D₉₅₉)⋊C₉

Splittings

derived, Hall	C₇×C₁₃₇ ⋊ C₂²×C₉
Hall	C₇⋊C₉×C₁₃₇ ⋊ C₂²
Hall	C₂×D₉₅₉ ⋊ C₉
Sylow	C₁₃₇ ⋊ C₂×D₇⋊C₉
Hall	C₇⋊C₉ ⋊ C₂×D₁₃₇
Sylow	C₇ ⋊ C₂×C₉×D₁₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₃₇
commutator, hypocenter	C₇×C₁₃₇	C₂²×C₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)⋊D₁₃₇
Fitting, socle	C₂×C₃×C₇×C₁₃₇	C₂×C₃
prime radical	C₂×C₃×D₉₅₉	C₃
cosocle	C₃×C₇×C₁₃₇	C₂²×C₃
LCS	G ▷ C₇×C₁₃₇
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17262

Conjugacy classes & character table

2082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34524, 18);