C₂²×C₁₃×#127 #13112498

order	1664
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂²×C₁₃×#127

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

3000 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 5 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2172);