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C₃×D₃×D₄₃ #13095440

order	1548
isoclinism	isoclinic class of D₃×D₄₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₃×D₃×D₄₃

Splittings

Fitting, socle, Hall	C₃²×C₄₃ ⋊ C₂²
derived	C₃×C₄₃ ⋊ C₂²×C₃
Sylow	C₄₃ ⋊ C₂×C₃×D₃
Sylow	C₃² ⋊ C₂×D₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	D₃×D₄₃
commutator, cosocle, hypocenter	C₃×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₄₃	C₂²
LCS	G ▷ C₃×C₄₃
UCS	C₁ ◁ C₃

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 258

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₃×D₄₃⋊C₇, D₄₃×C₃⋊AGL(1,𝔽₇), D₃×ΓL(1,𝔽₈)⋊D₄₃, …
maximal normal subgroup of	C₃×D₃×D₄₃⋊C₇, C₃×D₃×C₇×D₄₃, C₃×D₃×C₁₁×D₄₃, …
maximal quotient of	D₄₃×C₃⋊AGL(1,𝔽₇), D₃×ΓL(1,𝔽₈)⋊D₄₃, (C₃⋊AGL(1,𝔽₇))⋊D₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1548, 33);