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D₃×D₄₉₃ #20238331

order	5916
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₄₉₃
unambiguous semidirect product	(D₃×C₁₇)⋊D₂₉
unambiguous semidirect product	(D₃×C₂₉)⋊D₁₇

Splittings

Fitting, socle, derived, Hall	C₃×C₁₇×C₂₉ ⋊ C₂²
Hall	C₁₇×C₂₉ ⋊ C₂×D₃
Hall	C₃×C₂₉ ⋊ C₂×D₁₇
Hall	C₃×C₁₇ ⋊ C₂×D₂₉
Sylow	C₂₉ ⋊ D₃×D₁₇
Sylow	C₁₇ ⋊ D₃×D₂₉
Sylow	C₃ ⋊ C₂×D₄₉₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₁₇×C₂₉	C₂²
LCS	G ▷ C₃×C₁₇×C₂₉
UCS	C₁

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

744 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₉×D₄₉₃, C₃×D₃×D₄₉₃, C₃⋊D₃×D₄₉₃, …
maximal normal subgroup of	C₃×D₃×D₄₉₃, C₅×D₃×D₄₉₃
maximal quotient of	D₉×D₄₉₃, C₃×D₃×D₄₉₃, C₃⋊D₃×D₄₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5916, 27);