C₁₃×#2642 #13111700

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₃×#2642

Subgroups

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

416 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 41
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(20,24)(22,25)(27,31)(32,34)(33,39)(40,41);(14,15,16,17)(18,19,21,23)(20,22,24,25)(26,27)(28,34)(29,33)(30,31)(32,36)(35,41)(37,40)(38,39);(14,15)(16,17)(18,20)(19,22)(21,24)(23,25)(26,28,30,36)(27,32,31,34)(29,37,38,35)(33,41,39,40);(26,29,30,38)(27,33,31,39)(28,35,36,37)(32,40,34,41)

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15764310, #15764366, #15838142, …
maximal subgroup of	C₁₃×#10095, C₁₃×#10103, C₁₃×#18441, …
maximal normal subgroup of	C₁₃×#10095, C₁₃×#10103, C₁₃×#18441, …
maximal quotient of	C₁₃×#14261, C₁₃×#14274, C₁₃×#14283, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1374);