C₁₃×#1450 #13110508

order	1664
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₁₃ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₁₃×#1450

Subgroups

	subgroup	G/H
center	C₄×C₈×C₁₃	C₂²
commutator	C₂	C₂×C₄×C₈×C₁₃
Frattini, cosocle	C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₄²
prime radical	C₂³×C₁₃	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₁₃ ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 832

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

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

Conjugacy classes & character table

1040 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	#15749755, #15749758, #15749786, …
maximal subgroup of	C₁₃×#7140, C₁₃×#7141, C₁₃×#7153, …
maximal normal subgroup of	C₁₃×#7140, C₁₃×#7141, C₁₃×#7153, …
maximal quotient of	C₁₃×#7841, C₁₃×#7849, C₁₃×#8133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 182);

C13×#1450 #13110508