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C₃×D₁₁₁₉ #20269558

order	6714
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₁₁₁₉
unambiguous semidirect product	C₃⋊(C₃×D₃₇₃)

Splittings

Fitting, socle, Hall	C₃²×C₃₇₃ ⋊ C₂
derived	C₃×C₃₇₃ ⋊ C₂×C₃
Sylow	C₃₇₃ ⋊ C₃×D₃
Sylow	C₃² ⋊ D₃₇₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₁₁₁₉
commutator, hypocenter	C₃×C₃₇₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₃₇₃	C₂
LCS	G ▷ C₃×C₃₇₃
UCS	C₁ ◁ C₃

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1683 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×D₃₇₃, D₃×D₁₁₁₉, (C₃⋊D₃)⋊D₃₇₃, …
maximal normal subgroup of	C₃×D₃×D₃₇₃, D₃×D₁₁₁₉, (C₃⋊D₃)⋊D₃₇₃, …
maximal quotient of	C₃×Dic₁₁₁₉, C₂×C₃×D₁₁₁₉, C₃×C₅×D₁₁₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6714, 14);