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C₂×D₇×C₄₁⋊C₅ #19153252

order	5740
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₇×C₄₁⋊C₅
unambiguous semidirect product	C₇⋊(C₂²×C₄₁⋊C₅)
unambiguous semidirect product	(C₂×C₇)⋊(C₂×C₄₁⋊C₅)
unambiguous semidirect product	(C₂×D₇×C₄₁)⋊C₅

Splittings

Fitting, socle	C₂×C₇×C₄₁ ⋊ C₂×C₅
derived, Hall	C₇×C₄₁ ⋊ C₂²×C₅
Hall	C₇×C₄₁⋊C₅ ⋊ C₂²
Hall	C₂×D₇×C₄₁ ⋊ C₅
Sylow	C₄₁ ⋊ C₂×C₅×D₇
Sylow	C₇ ⋊ C₂²×C₄₁⋊C₅

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇×C₄₁⋊C₅
commutator, hypocenter	C₇×C₄₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₄₁	C₂×C₅
LCS	G ▷ C₇×C₄₁
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

130 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×AGL(1,𝔽₇)×C₄₁⋊C₅, D₃×D₇×C₄₁⋊C₅, C₂×C₃×D₇×C₄₁⋊C₅, …
maximal normal subgroup of	C₂×AGL(1,𝔽₇)×C₄₁⋊C₅, C₂×C₃×D₇×C₄₁⋊C₅, C₂×C₅×D₇×C₄₁⋊C₅
maximal quotient of	D₃×D₇×C₄₁⋊C₅, C₂×C₃×D₇×C₄₁⋊C₅, C₂×D₂₁×C₄₁⋊C₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5740, 19);