Finite Group Databasebeta

← Prev (#13131389) Next (#13131391) →

C₂×M₁₆×#261 #13131390

order	1664
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₂×M₁₆×#261

Splittings

Fitting	C₂×C₁₃×M₁₆ ⋊ C₄
Sylow	C₁₃ ⋊ C₂×C₄×M₁₆

Subgroups

	subgroup	G/H
center	C₂×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂²×C₄²
Frattini	C₄	C₂³×#261
Fitting	C₂×C₁₃×M₁₆	C₄
socle	C₂²×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₂×C₄
cosocle	C₄×D₁₃	C₂⁴
hypercenter	C₂×M₁₆	#261
hypocenter	C₁₃	C₂×C₄×M₁₆
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 208

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#261×H(3,ℤ/4), #261×#338, #261×#339, …
maximal normal subgroup of	#261×H(3,ℤ/4), #261×#338, #261×#339, …
maximal quotient of	C₂×M₁₆×#1057, M₁₆×D₁₃⋊C₈, C₂×#13130034, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 21064);