C₁₃×#10494 #15696833

order	3328
nilpotency class	3
isoclinism	isoclinic class of #10488
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#10494

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂³×C₁₃	#123
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 344 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)(14,15,18,22)(16,23,24,20)(17,19,26,21)(25,28,29,27)(30,31)(32,35)(33,36)(34,38)(37,42)(39,43)(40,45)(41,44);(15,19)(16,24)(17,26)(20,28)(21,22)(23,27)(30,32,34,40)(31,35,38,45)(33,41,42,39)(36,44,37,43);(14,16,17,25,18,24,26,29)(15,20,21,28,22,23,19,27)(31,36)(33,42)(35,43)(37,38)(39,41)(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, 3482);