C₁₃⋊D₁₃ #66764

order	338
isoclinism	isoclinic class of C₁₃⋊D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁₃

Aliases

C₁₃⋊D₁₃

C₁₃² ⋊ C₂

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²	C₂
LCS	G ▷ C₁₃²
UCS	C₁

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 169

A minimal faithful permutation representation — 3 generators on 26 points:

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

Polycyclic presentation:

2,13^2|b^a=b^12,c^a=c^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(338, 4);