Finite Group Databasebeta

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C₂×(C₇⋊C₉)⋊D₁₀₇ #41004067

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

Aliases

direct product	C₂×(C₇⋊C₉)⋊D₁₀₇
unambiguous semidirect product	(C₂×C₇⋊C₉)⋊D₁₀₇
unambiguous semidirect product	(C₂×C₁₀₇)⋊(D₇⋊C₉)
unambiguous semidirect product	(C₂×D₇₄₉)⋊C₉

Splittings

derived, Hall	C₇×C₁₀₇ ⋊ C₂²×C₉
Hall	C₇⋊C₉×C₁₀₇ ⋊ C₂²
Hall	C₂×D₇₄₉ ⋊ C₉
Sylow	C₁₀₇ ⋊ C₂×D₇⋊C₉
Hall	C₇⋊C₉ ⋊ C₂×D₁₀₇
Sylow	C₇ ⋊ C₂×C₉×D₁₀₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	ΓL(1,𝔽₈)⋊D₁₀₇
commutator, hypocenter	C₇×C₁₀₇	C₂²×C₉
Frattini	C₃	C₂×ΓL(1,𝔽₈)⋊D₁₀₇
Fitting, 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×C₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13482

Conjugacy classes & character table

1632 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26964, 16);