Finite Group Databasebeta

← Prev (#23758475) Next (#23758477) →

C₃×(C₄₃⋊C₃)⋊D₁₃ #23758476

order	10062
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×(C₄₃⋊C₃)⋊D₁₃
unambiguous semidirect product	(C₄₃⋊C₃)⋊(C₃×D₁₃)

Splittings

Fitting, socle	C₃×C₁₃×C₄₃ ⋊ C₂×C₃
derived, Hall	C₁₃×C₄₃ ⋊ C₂×C₃²
Hall	C₃×C₁₃×C₄₃⋊C₃ ⋊ C₂
Hall	D₅₅₉ ⋊ C₃²
Hall	C₃×C₄₃⋊C₃ ⋊ D₁₃
Sylow	C₄₃ ⋊ C₃²×D₁₃
Sylow	C₁₃ ⋊ C₃×D₄₃⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	(C₄₃⋊C₃)⋊D₁₃
commutator, cosocle, hypocenter	C₁₃×C₄₃	C₂×C₃²
Frattini	C₁	G
Fitting, socle	C₃×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₁₃×C₄₃
UCS	C₁ ◁ C₃

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

345 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×D₁₃×D₄₃⋊C₃, D₃×(C₄₃⋊C₃)⋊D₁₃, (C₃⋊(D₄₃⋊C₃))⋊D₁₃, …
maximal normal subgroup of	C₃×D₁₃×D₄₃⋊C₃, D₃×(C₄₃⋊C₃)⋊D₁₃, (C₃⋊(D₄₃⋊C₃))⋊D₁₃, …
maximal quotient of	C₃×(C₄₃⋊C₃)⋊Dic₁₃, C₂×C₃×(C₄₃⋊C₃)⋊D₁₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10062, 40);