C₁₃×#2031 #13111089

order	1664
nilpotency class	3
isoclinism	isoclinic class of #2031
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#2031

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle	C₂×C₁₃	#393
prime radical	C₂×C₁₃×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

244 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 80 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) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

338 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#2031, #15890347, #15893797, …
maximal subgroup of	C₂×C₁₃×#2031, C₁₃×#23472, C₁₃×#23833, …
maximal normal subgroup of	C₂×C₁₃×#2031, C₁₃×#23472, C₁₃×#23833, …
maximal quotient of	C₁₃×#10362, C₁₃×#10363, C₁₃×#10364, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 763);