C₂²×C₁₃×#120 #13112489

order	1664
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂¹¹

Aliases

C₂²×C₁₃×#120

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

4544 conjugacy classes of subgroups; only the 1112 normal subgroups are shown.

normal subgroups only

This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 1112 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 416

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);(5,6)(7,9)(8,10)(11,12);(6,9)(10,12);(6,10)(9,12)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2163);