C₁₃×#10525 #15696864

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10524
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#10525

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₁₃×#3253	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

370 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 90 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)(14,15)(16,20)(17,19)(18,22)(21,25)(23,26)(24,27)(28,29)(31,36)(32,39)(33,34)(37,40)(38,43)(41,42);(15,19)(16,23)(17,25)(20,27)(21,22)(24,29)(30,31)(32,40)(33,43)(34,36)(35,38)(37,42)(39,45)(41,44);(14,16,17,23,18,24,25,29)(15,20,21,28,22,27,19,26)(30,32,34,39,35,42,33,41)(31,37,43,45,38,40,36,44)

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, 3513);