C₁₃×#9425 #15695764

order	3328
nilpotency class	3
isoclinism	isoclinic class of #9415
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9425

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#386
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

534 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 118 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)(14,15,18,25,30,42,16,28)(17,33,36,43,34,22,31,39)(19,26,29,21,20,27,32,23)(24,44,41,35,40,45,38,37);(15,21,26,25)(16,29)(17,34)(18,32)(22,38,24,43)(23,27,28,42)(31,44)(33,41,40,39)(35,37)(36,45);(15,22)(16,18)(17,35)(21,38)(23,41)(24,26)(25,43)(27,40)(28,39)(29,32)(31,45)(33,42)(34,37)(36,44)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2413);