D₁₆×C₁₀₇ #16811981

order	3424
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₀₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

D₁₆×C₁₀₇

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₇	D₈
commutator, Frattini, cosocle	C₈	C₂²×C₁₀₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₇ ◁ C₄×C₁₀₇ ◁ C₈×C₁₀₇ ◁ G

28 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 123
transitive degree	μ_t(G) = 1712

A minimal faithful permutation representation — 2 generators on 123 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(2,16)(3,15)(4,14)(5,13)(6,12)(7,11)(8,10)

Conjugacy classes & character table

1177 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃₂×C₁₀₇, SD₆₄×C₁₀₇, C₂×D₁₆×C₁₀₇, …
maximal normal subgroup of	D₃₂×C₁₀₇, SD₆₄×C₁₀₇, C₂×D₁₆×C₁₀₇, …
maximal quotient of	#357×C₁₀₇, #366×C₁₀₇, D₃₂×C₁₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3424, 18);

D16×C107 #16811981