Finite Group Databasebeta

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C₂×C₇×D₇×C₄₁ #22548823

order	8036
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₄₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₇×D₇×C₄₁
unambiguous semidirect product	C₇⋊(C₂²×C₇×C₄₁)
unambiguous semidirect product	(C₂×C₇)⋊(C₂×C₇×C₄₁)

Splittings

Fitting, socle	C₂×C₇²×C₄₁ ⋊ C₂
derived	C₇ ⋊ C₂²×C₇×C₄₁
Hall	C₇²×C₄₁ ⋊ C₂²
Sylow	C₇² ⋊ C₂²×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₇×C₄₁	D₇
commutator, hypocenter	C₇	C₂²×C₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₄₁	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₇×C₄₁

52 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2870 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄₁×#64418, C₂×C₇×C₄₁×AGL(1,𝔽₇), C₂×D₇×ΓL(1,𝔽₈)×C₄₁, …
maximal normal subgroup of	C₂×C₇×C₄₁×AGL(1,𝔽₇), C₂×D₇×ΓL(1,𝔽₈)×C₄₁, C₂×C₄₁×#64423, …
maximal quotient of	D₃×C₇×D₇×C₄₁, C₂×C₃×C₇×D₇×C₄₁, C₂×C₇×C₄₁×D₂₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8036, 33);