C₁₃×#10611 #15696950

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

Aliases

direct product

C₁₃×#10611

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#396
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 328 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)(14,15,17,23,19,21,18,22)(16,24,25,20,27,28,26,29)(30,31)(32,40)(33,38)(34,37)(35,39)(36,42)(41,44)(43,45);(14,16,17,25,19,27,18,26)(15,20,22,24,21,29,23,28)(30,32,33,42,35,41,34,43)(31,36,37,40,39,45,38,44);(15,21)(16,25)(17,18)(20,28)(24,29)(26,27)(31,37)(32,41)(33,34)(36,40)(38,39)(44,45)

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, 3599);