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D₃×D₆₂₉ #21419554

order	7548
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₆₂₉
unambiguous semidirect product	(D₃×C₁₇)⋊D₃₇
unambiguous semidirect product	(D₃×C₃₇)⋊D₁₇

Splittings

Fitting, socle, derived, Hall	C₃×C₁₇×C₃₇ ⋊ C₂²
Hall	C₁₇×C₃₇ ⋊ C₂×D₃
Hall	C₃×C₃₇ ⋊ C₂×D₁₇
Hall	C₃×C₁₇ ⋊ C₂×D₃₇
Sylow	C₃₇ ⋊ D₃×D₁₇
Sylow	C₁₇ ⋊ D₃×D₃₇
Sylow	C₃ ⋊ C₂×D₆₂₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇×C₃₇	C₂²
LCS	G ▷ C₃×C₁₇×C₃₇
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

948 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×D₆₂₉, D₃×C₁₇⋊(D₃₇⋊C₃), C₃×D₃×D₆₂₉, …
maximal normal subgroup of	D₃×C₁₇⋊(D₃₇⋊C₃), C₃×D₃×D₆₂₉, C₅×D₃×D₆₂₉
maximal quotient of	D₉×D₆₂₉, C₃×D₃×D₆₂₉, D₃×D₁₈₈₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7548, 41);