C₁₃×#10614 #15696953

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10611
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#10614

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#126
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

276 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 98 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)(14,15,20,23,19,24,18,28)(16,25,27,29,17,22,26,21)(30,31)(32,34)(33,41)(35,38)(36,39)(37,43)(40,44)(42,45);(14,16,20,27,19,17,18,26)(15,21,28,22,24,29,23,25)(30,32,35,39,36,38,34,31)(33,40,43,37,44,41,42,45);(14,17,19,16)(15,22,24,25)(18,26,20,27)(21,23,29,28)(30,33,36,44)(31,37,39,45)(32,40,38,41)(34,43,35,42)

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, 3602);