C₁₃×#2061 #13111119

order	1664
nilpotency class	3
isoclinism	isoclinic class of #2002
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#2061

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

230 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20)(16,21,17,19)(22,23,25,29)(24,31,32,27)(26,28,34,30)(33,37,35,36);(14,16,18,17)(15,19,20,21)(22,24,25,32)(23,27,29,31)(26,35,34,33)(28,37,30,36);(14,17,18,16)(15,19,20,21)(23,28)(26,34)(27,36)(29,30)(31,37)(33,35)

Conjugacy classes & character table

338 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15750546, #15775834, #15775848, …
maximal subgroup of	C₁₃×#7442, C₁₃×#12235, C₁₃×#12237, …
maximal normal subgroup of	C₁₃×#7442, C₁₃×#12235, C₁₃×#12237, …
maximal quotient of	C₁₃×#10568, C₁₃×#10569, C₁₃×#10571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 793);