C₁₃×#2634 #13111692

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

Aliases

direct product

C₁₃×#2634

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 192 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 192 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)(19,22)(23,25)(26,27,31,29)(28,34,36,32)(30,33,38,37)(35,40,41,39);(15,17)(19,22)(23,25)(26,28,31,36)(27,32,29,34)(30,35,38,41)(33,39,37,40);(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,29,31,27)(28,32,36,34)(30,33,38,37)(35,40,41,39);(18,20,21,24)(19,23,22,25)(26,30)(27,33)(28,35)(29,37)(31,38)(32,39)(34,40)(36,41)

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15758918, #15763816, #15763844, …
maximal subgroup of	C₁₃×#9190, C₁₃×#10021, C₁₃×#10025, …
maximal normal subgroup of	C₁₃×#9190, C₁₃×#10021, C₁₃×#10025, …
maximal quotient of	C₁₃×#14270, C₁₃×#14289, C₁₃×#14298, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1366);