C₁₃×#10023 #15696362

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10018
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#10023

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 518 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) = 832

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

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 3011);