C₁₃×#1798 #13110856

order	1664
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#1798

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂³
commutator	C₂³	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₃
socle	C₂³×C₁₃	C₂²×C₄
prime radical	C₂⁴×C₁₃	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

312 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 832

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

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15750044, #15750047, #15754757, …
maximal subgroup of	C₁₃×#7252, C₁₃×#7253, C₁₃×#8409, …
maximal normal subgroup of	C₁₃×#7252, C₁₃×#7253, C₁₃×#8409, …
maximal quotient of	C₁₃×#8561, C₁₃×#8562, C₁₃×#8567, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 530);