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C₂×(C₆₁⋊C₃)⋊D₁₃ #23748955

order	9516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×(C₆₁⋊C₃)⋊D₁₃
unambiguous semidirect product	(C₂×C₆₁⋊C₃)⋊D₁₃

Splittings

Fitting, socle	C₂×C₁₃×C₆₁ ⋊ C₂×C₃
derived, Hall	C₁₃×C₆₁ ⋊ C₂²×C₃
Hall	C₂×D₇₉₃ ⋊ C₃
Hall	C₁₃×C₆₁⋊C₃ ⋊ C₂²
Hall	C₆₁⋊C₃ ⋊ C₂×D₁₃
Sylow	C₆₁ ⋊ C₂×C₃×D₁₃
Sylow	C₁₃ ⋊ C₂×D₆₁⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	(C₆₁⋊C₃)⋊D₁₃
commutator, cosocle, hypocenter	C₁₃×C₆₁	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₆₁	C₂×C₃
LCS	G ▷ C₁₃×C₆₁
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

308 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×(C₁₃⋊C₃)⋊(D₆₁⋊C₃), D₃×(C₆₁⋊C₃)⋊D₁₃, C₂×C₃×(C₆₁⋊C₃)⋊D₁₃, …
maximal normal subgroup of	C₂×(C₁₃⋊C₃)⋊(D₆₁⋊C₃), C₂×C₃×(C₆₁⋊C₃)⋊D₁₃
maximal quotient of	C₂×(C₆₁⋊C₉)⋊D₁₃, D₃×(C₆₁⋊C₃)⋊D₁₃, C₂×C₃×(C₆₁⋊C₃)⋊D₁₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9516, 64);