C₁₃×#8744 #15695083

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8738
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#8744

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#381
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

384 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 110 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)(16,23,25,19)(17,22)(18,21)(20,24,27,29)(26,28)(30,31,33,37,34,36,40,43)(32,35,38,42,39,41,44,45);(14,16)(15,19)(17,24)(18,25)(20,22)(21,23)(26,29)(27,28)(30,32,34,39)(31,35,36,41)(33,38,40,44)(37,42,43,45);(14,16)(15,20,21,27)(17,24)(18,25)(19,22,23,28)(26,29)(31,36)(33,40)(35,41)(38,44)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1732);