C₁₃×#9436 #15695775

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9431
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9436

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#123
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

400 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 1664

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

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

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, 2424);