C₁₃×#13429 #15699768

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13429
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#13429

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#2044
commutator, Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#3199	C₂
LCS	G ▷ C₂×#41 ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

434 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 86 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)(16,25)(17,20)(18,23)(19,24)(21,28)(22,29)(26,38)(27,42)(30,34)(31,36)(32,39)(33,43)(35,45)(37,44)(40,41);(15,20)(16,26)(17,29)(21,33)(22,24)(23,34)(25,40)(30,44)(35,36)(37,39)(38,42)(43,45);(14,16,17,27,19,26,29,41)(15,21,22,35,24,36,20,33)(18,31,30,45,32,28,44,43)(23,38,37,42,39,25,34,40)

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6417);