C₁₃×#1937 #13110995

order	1664
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#1937

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle	C₂²×C₁₃	C₄×D₄
prime radical	C₂×C₁₃×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

230 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 33
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#1937, #15865665, #15865674, …
maximal subgroup of	C₂×C₁₃×#1937, C₁₃×#21098, C₁₃×#21099, …
maximal normal subgroup of	C₂×C₁₃×#1937, C₁₃×#21098, C₁₃×#21099, …
maximal quotient of	C₁₃×#9553, C₁₃×#9554, C₁₃×#9559, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 669);