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C₉×D₇×C₁₄₉ #34037366

order	18774
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₄₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×D₇×C₁₄₉

Splittings

Fitting, Hall	C₇×C₉×C₁₄₉ ⋊ C₂
derived, Sylow	C₇ ⋊ C₂×C₉×C₁₄₉
Hall	C₇×C₁₄₉ ⋊ C₂×C₉
Hall	C₇×C₉ ⋊ C₂×C₁₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₄₉	D₇
commutator, hypocenter	C₇	C₂×C₉×C₁₄₉
Frattini	C₃	C₃×D₇×C₁₄₉
Fitting	C₇×C₉×C₁₄₉	C₂
socle	C₃×C₇×C₁₄₉	C₂×C₃
prime radical	C₃×D₇×C₁₄₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₄₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₉×C₁₄₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 9387

Conjugacy classes & character table

6705 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₇×D₁₄₉, D₇×D₉×C₁₄₉, D₇×D₁₃₄₁, …
maximal normal subgroup of	C₉×D₇×D₁₄₉, D₇×D₉×C₁₄₉, D₇×D₁₃₄₁, …
maximal quotient of	C₉×Dic₇×C₁₄₉, C₂×C₉×D₇×C₁₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18774, 4);