Finite Group Databasebeta

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C₂×(C₇⋊C₉)⋊D₁₄₉ #49176299

order	37548
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₇⋊C₉)⋊D₁₄₉
unambiguous semidirect product	(C₂×C₇⋊C₉)⋊D₁₄₉
unambiguous semidirect product	(C₂×C₁₄₉)⋊(D₇⋊C₉)
unambiguous semidirect product	(C₂×D₁₀₄₃)⋊C₉

Splittings

derived, Hall	C₇×C₁₄₉ ⋊ C₂²×C₉
Hall	C₇⋊C₉×C₁₄₉ ⋊ C₂²
Hall	C₂×D₁₀₄₃ ⋊ C₉
Sylow	C₁₄₉ ⋊ C₂×D₇⋊C₉
Hall	C₇⋊C₉ ⋊ C₂×D₁₄₉
Sylow	C₇ ⋊ C₂×C₉×D₁₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₄₉
commutator, hypocenter	C₇×C₁₄₉	C₂²×C₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)⋊D₁₄₉
Fitting, socle	C₂×C₃×C₇×C₁₄₉	C₂×C₃
prime radical	C₂×C₃×D₁₀₄₃	C₃
cosocle	C₃×C₇×C₁₄₉	C₂²×C₃
LCS	G ▷ C₇×C₁₄₉
UCS	C₁ ◁ C₂×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 18774

Conjugacy classes & character table

2262 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37548, 18);