C₂×C₁₃×#124 #11719561

order	832
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

C₂×C₁₃×#124

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

330 conjugacy classes of subgroups.

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 27 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1527);