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C₃×D₁₃₇₁ #22551709

order	8226
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₁₃₇₁
unambiguous semidirect product	C₃⋊(C₃×D₄₅₇)

Splittings

Fitting, socle, Hall	C₃²×C₄₅₇ ⋊ C₂
derived	C₃×C₄₅₇ ⋊ C₂×C₃
Sylow	C₄₅₇ ⋊ C₃×D₃
Sylow	C₃² ⋊ D₄₅₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₁₃₇₁
commutator, hypocenter	C₃×C₄₅₇	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₄₅₇	C₂
LCS	G ▷ C₃×C₄₅₇
UCS	C₁ ◁ C₃

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2061 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×D₄₅₇, D₃×D₁₃₇₁, (C₃⋊D₃)⋊D₄₅₇, …
maximal normal subgroup of	C₃×D₃×D₄₅₇, D₃×D₁₃₇₁, (C₃⋊D₃)⋊D₄₅₇, …
maximal quotient of	C₃×Dic₁₃₇₁, C₂×C₃×D₁₃₇₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8226, 14);