C₂×C₁₃×#395 #13111445

order	1664
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₃×#395

Subgroups

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

908 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 360 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) = 31
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15757914, #15757919, #15763136, …
maximal subgroup of	C₁₃×#9014, C₁₃×#9015, C₁₃×#9917, …
maximal normal subgroup of	C₁₃×#9014, C₁₃×#9015, C₁₃×#9917, …
maximal quotient of	C₂×C₁₃×#1441, C₂×C₁₃×#1444, C₂×C₁₃×#1446, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1119);