C₁₃×#2983 #13112041

order	1664
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2983

Subgroups

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

356 conjugacy classes of subgroups; only the 268 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 268 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 — 4 generators on 37 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15756796, #15756961, #15757589, …
maximal subgroup of	C₁₃×#8838, C₁₃×#8865, C₁₃×#8962, …
maximal normal subgroup of	C₁₃×#8838, C₁₃×#8865, C₁₃×#8962, …
maximal quotient of	C₁₃×#20534, C₁₃×#20536, C₁₃×#20570, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1715);