Finite Group Databasebeta

← Prev (#88166) Next (#88168) →

SD₁₆×D₁₃ #88167

order	416
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

SD₁₆×D₁₃

Splittings

Fitting	C₁₃×SD₁₆ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×SD₁₆

Subgroups

	subgroup	G/H
center	C₂	D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₁₃
Fitting	C₁₃×SD₁₆	C₂
socle	C₂×C₁₃	C₂×D₄
prime radical	D₄×D₁₃	C₂
hypercenter	SD₁₆	D₁₃
hypocenter	C₁₃	C₂×SD₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 104

A minimal faithful permutation representation — 3 generators on 21 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13);(1,2,4,6,8,10,12,13,11,9,7,5,3)(15,18)(16,21)(19,20);(14,15,17,20)(16,18,21,19)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₁₆×#261, #11719106, C₂×SD₁₆×D₁₃, …
maximal normal subgroup of	SD₁₆×#261, #11719106, C₂×SD₁₆×D₁₃, …
maximal quotient of	#11718419, #11718421, #11718422, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 134);