C₁₃×#2402 #13111460

order	1664
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#2402

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂³
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
socle, prime radical	C₂³×C₁₃	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

400 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 37
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15766054, #15766059, #15871263, …
maximal subgroup of	C₁₃×#10372, C₁₃×#10373, C₁₃×#21676, …
maximal normal subgroup of	C₁₃×#10372, C₁₃×#10373, C₁₃×#21676, …
maximal quotient of	C₁₃×#13846, C₁₃×#13848, C₁₃×#13854, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1134);