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D₈×D₁₃ #88164

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

Aliases

D₈×D₁₃

Splittings

Fitting	C₁₃×D₈ ⋊ C₂
Sylow	C₁₃ ⋊ C₂×D₈

Subgroups

	subgroup	G/H
center	C₂	D₄×D₁₃
commutator, cosocle	C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₁₃
Fitting	C₁₃×D₈	C₂
socle	C₂×C₁₃	C₂×D₄
hypercenter	D₈	D₁₃
hypocenter	C₁₃	C₂×D₈
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

76 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)(16,18)(17,20)(19,21)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11718276, #11718278, D₁₃×D₁₆, …
maximal normal subgroup of	#11718276, #11718278, D₁₃×D₁₆, …
maximal quotient of	#11718417, #11718420, #11718421, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 131);