Finite Group Databasebeta

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C₂×C₉×D₇₄₉ #41004083

order	26964
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₉×D₇₄₉
unambiguous semidirect product	(C₂×C₁₀₇)⋊(C₉×D₇)

Splittings

Fitting	C₂×C₇×C₉×C₁₀₇ ⋊ C₂
derived, Hall	C₇×C₁₀₇ ⋊ C₂²×C₉
Hall	C₇×C₉×C₁₀₇ ⋊ C₂²
Hall	C₉×C₁₀₇ ⋊ C₂×D₇
Sylow	C₁₀₇ ⋊ C₂×C₉×D₇
Hall	C₇×C₉ ⋊ C₂×D₁₀₇
Sylow	C₇ ⋊ C₂×C₉×D₁₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₇₄₉
commutator, hypocenter	C₇×C₁₀₇	C₂²×C₉
Frattini	C₃	C₂×C₃×D₇₄₉
Fitting	C₂×C₇×C₉×C₁₀₇	C₂
socle	C₂×C₃×C₇×C₁₀₇	C₂×C₃
prime radical	C₂×C₃×D₇₄₉	C₃
cosocle	C₃×C₇×C₁₀₇	C₂²×C₃
LCS	G ▷ C₇×C₁₀₇
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13482

Conjugacy classes & character table

6768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26964, 32);