C₁₃×#9003 #15695342

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#9003

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

578 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 134 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 — 3 generators on 41 points:

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

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1991);