C₁₃×#1940 #13110998

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

Aliases

direct product

C₁₃×#1940

Subgroups

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

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

normal subgroups only

This group has 248 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) = 29
transitive degree	μ_t(G) = 1664

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)(16,17)(19,21)(22,23,27,24,26,28,25,29);(15,17)(22,24,27,28,26,29,25,23);(18,19,20,21)(22,25,26,27)(23,24,28,29)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15749719, #15757050, #15757057, …
maximal subgroup of	C₁₃×#7124, C₁₃×#8878, C₁₃×#8879, …
maximal normal subgroup of	C₁₃×#7124, C₁₃×#8878, C₁₃×#8879, …
maximal quotient of	C₁₃×#9597, C₁₃×#9598, C₁₃×#9599, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 672);