C₂×C₁₃×D₁₆ #11719040

order	832
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₁₃×D₁₆

	subgroup	G/H
center, socle	C₂²×C₁₃	D₈
commutator, Frattini, cosocle	C₈	C₂³×C₁₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₈×C₁₃ ◁ G

98 conjugacy classes of subgroups.

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 31 points:

(1,2)(19,20,21,22,23,24,25,26,27,28,29,30,31);(3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18);(4,18)(5,17)(6,16)(7,15)(8,14)(9,13)(10,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1006);