C₁₃×#13074 #15699413

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₃×#13074

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₁₃×#3058	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

490 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 490 conjugacy classes of subgroups — too many to draw. Only its 146 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,22,31,38)(18,33)(19,25)(20,36)(21,24)(23,27)(28,42,40,41)(29,35)(30,44,34,45)(32,43,37,39);(14,16,27,25,20,29,35,36,19,23,26,15,21,33,18,24)(17,28,42,38,32,44,30,43,31,40,41,22,37,45,34,39);(14,17)(15,22)(16,28)(18,34)(19,31)(20,32)(21,37)(23,40)(24,39)(25,38)(26,41)(27,42)(29,44)(30,35)(33,45)(36,43)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6062);