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C₂×C₇⋊C₉×C₁₄₉ #34037364

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

Aliases

direct product	C₂×C₇⋊C₉×C₁₄₉
unambiguous semidirect product	(C₂×C₇)⋊(C₉×C₁₄₉)
unambiguous semidirect product	(C₂×C₇×C₁₄₉)⋊C₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₄₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₂×C₉×C₁₄₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)×C₁₄₉
Fitting, socle, prime radical	C₂×C₃×C₇×C₁₄₉	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₄₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₄₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18774

Conjugacy classes & character table

4470 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₇⋊C₉×C₁₄₉, C₇⋊C₉×Dic₁₄₉, C₁₄₉×Dic₇⋊C₉, …
maximal normal subgroup of	C₄×C₇⋊C₉×C₁₄₉, C₇⋊C₉×Dic₁₄₉, C₁₄₉×Dic₇⋊C₉, …
maximal quotient of	C₄×C₇⋊C₉×C₁₄₉, C₂²×C₇⋊C₉×C₁₄₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18774, 2);