#88040

order	416
isoclinism	isoclinic class of D₂₀₈
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting	C₁₃×C₁₆ ⋊ C₂
Sylow	C₁₃ ⋊ SD₃₂

Subgroups

	subgroup	G/H
center	C₂	D₁₀₄
commutator, cosocle	C₈×C₁₃	C₂²
Frattini	C₈	C₂×D₁₃
Fitting	C₁₃×C₁₆	C₂
socle	C₂×C₁₃	D₈
prime radical	D₁₀₄	C₂
hypercenter	C₁₆	D₁₃
hypocenter	C₁₃	SD₃₂
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆

26 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,4,6,8,10,12,13,11,9,7,5,3)(14,15,20,26,25,29,16,19,18,22,23,28,17,21,24,27);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(15,19)(16,23)(17,25)(20,24)(21,28)(22,27)(26,29)

Polycyclic presentation:

2^5,13|b^2=cd,c^2=d,d^2=e,b^a=bc,c^a=cde,d^a=de,f^a=f^12

Conjugacy classes & character table

107 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#88040, #11718565, #11718569, …
maximal normal subgroup of	C₂×#88040, #11718565, #11718569, …
maximal quotient of	#11718095, #11718097, #11718101, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(416, 7);