C₂×C₁₃×#127 #11719565

order	832
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

C₂×C₁₃×#127

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

498 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1531);