C₁₃×#2675 #13111733

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2668
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

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

804 conjugacy classes of subgroups; only the 224 normal subgroups are shown.

normal subgroups only

This group has 804 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 832

A minimal faithful permutation representation — 4 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1407);