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C₉×D₁₀₅₇ #34039745

order	19026
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₁₀₅₇

Splittings

Fitting, Hall	C₇×C₉×C₁₅₁ ⋊ C₂
derived, Hall	C₇×C₁₅₁ ⋊ C₂×C₉
Hall	C₉×C₁₅₁ ⋊ D₇
Sylow	C₁₅₁ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₁₅₁
Sylow	C₇ ⋊ C₉×D₁₅₁

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₀₅₇
commutator, hypocenter	C₇×C₁₅₁	C₂×C₉
Frattini	C₃	C₃×D₁₀₅₇
Fitting	C₇×C₉×C₁₅₁	C₂
socle, cosocle	C₃×C₇×C₁₅₁	C₂×C₃
prime radical	C₃×D₁₀₅₇	C₃
LCS	G ▷ C₇×C₁₅₁
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9513

Conjugacy classes & character table

4770 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₅₁, D₉×D₁₀₅₇, D₆₃⋊D₁₅₁, …
maximal normal subgroup of	C₉×D₇×D₁₅₁, D₉×D₁₀₅₇, D₆₃⋊D₁₅₁, …
maximal quotient of	C₉×Dic₁₀₅₇, C₂×C₉×D₁₀₅₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19026, 8);