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D₃×D₇×C₇₁ #20238552

order	5964
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₇×C₇₁
unambiguous semidirect product	(D₃×C₇)⋊(C₂×C₇₁)
unambiguous semidirect product	(C₃×D₇)⋊(C₂×C₇₁)
unambiguous semidirect product	D₂₁⋊(C₂×C₇₁)

Splittings

Fitting, socle, Hall	C₃×C₇×C₇₁ ⋊ C₂²
derived, Hall	C₃×C₇ ⋊ C₂²×C₇₁
Hall	C₇×C₇₁ ⋊ C₂×D₃
Hall	C₃×C₇₁ ⋊ C₂×D₇
Sylow	C₇ ⋊ C₂×D₃×C₇₁
Sylow	C₃ ⋊ C₂×D₇×C₇₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇₁	D₃×D₇
commutator, hypocenter	C₃×C₇	C₂²×C₇₁
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₇₁	C₂²
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₇₁

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1065 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₇×D₉×C₇₁, D₃×AGL(1,𝔽₇)×C₇₁, C₃×D₃×D₇×C₇₁, …
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×C₇₁, C₃×D₃×D₇×C₇₁, D₃×D₇×C₇₁⋊C₅, …
maximal quotient of	D₇×D₉×C₇₁, C₃×D₃×D₇×C₇₁, D₇×C₃⋊D₃×C₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5964, 31);