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D₃×C₂₉×D₂₁ #20300664

order	7308
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×C₂₉×D₂₁
unambiguous semidirect product	(C₃×D₃)⋊(D₇×C₂₉)
unambiguous semidirect product	(D₃×C₇)⋊(D₃×C₂₉)

Splittings

Fitting, socle, Hall	C₃²×C₇×C₂₉ ⋊ C₂²
derived, Hall	C₃²×C₇ ⋊ C₂²×C₂₉
Hall	C₃²×C₂₉ ⋊ C₂×D₇
Hall	C₇×C₂₉ ⋊ D₃²
Sylow	C₃² ⋊ C₂×D₇×C₂₉
Sylow	C₇ ⋊ D₃²×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂₉	D₃×D₂₁
commutator, hypocenter	C₃²×C₇	C₂²×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₂₉	C₂²
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂₉

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₅×D₃×C₂₉×D₂₁, D₃×C₂₉×D₁₀₅, C₂₉×D₁₅×D₂₁, …
maximal normal subgroup of	C₅×D₃×C₂₉×D₂₁
maximal quotient of	C₅×D₃×C₂₉×D₂₁, D₃×C₂₉×D₁₀₅, C₂₉×D₁₅×D₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 139);