Finite Group Databasebeta

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C₂×C₉×D₇×C₁₃₉ #46856027

order	35028
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₃₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₇×C₁₃₉

Splittings

Fitting	C₂×C₇×C₉×C₁₃₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂²×C₉×C₁₃₉
Hall	C₇×C₉×C₁₃₉ ⋊ C₂²
Hall	C₇×C₁₃₉ ⋊ C₂²×C₉
Hall	C₇×C₉ ⋊ C₂²×C₁₃₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₃₉	D₇
commutator, hypocenter	C₇	C₂²×C₉×C₁₃₉
Frattini	C₃	C₂×C₃×D₇×C₁₃₉
Fitting	C₂×C₇×C₉×C₁₃₉	C₂
socle	C₂×C₃×C₇×C₁₃₉	C₂×C₃
prime radical	C₂×C₃×D₇×C₁₃₉	C₃
cosocle	C₃×C₇	C₂²×C₃×C₁₃₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₉×C₁₃₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 17514

Conjugacy classes & character table

12510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35028, 63);