C₁₃×#1627 #13110685

order	1664
nilpotency class	3
isoclinism	isoclinic class of #1619
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#1627

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#120
commutator, Frattini, cosocle	C₄²	C₂³×C₁₃
prime radical	C₁₃×#459	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ G

250 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 76 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) = 29
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

338 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#1627, #15838680, #15838868, …
maximal subgroup of	C₂×C₁₃×#1627, C₁₃×#18494, C₁₃×#18516, …
maximal normal subgroup of	C₂×C₁₃×#1627, C₁₃×#18494, C₁₃×#18516, …
maximal quotient of	C₁₃×#7735, C₁₃×#7738, C₁₃×#7739, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 359);