C₁₃×#9028 #15695367

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

Aliases

direct product

C₁₃×#9028

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	#120
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁵×C₁₃	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

696 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 832

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)(18,19,23,24,22,20,21,25)(26,27)(28,31)(29,36,37,32)(30,33)(34,38,40,41)(35,39);(14,15,16,17)(18,20,22,19)(21,25,23,24)(26,28,30,35)(27,31,33,39)(29,34,37,40)(32,38,36,41);(18,21,22,23)(19,24,20,25)(26,29,30,37)(27,32,33,36)(28,34,35,40)(31,38,39,41)

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, 2016);