C₁₃×#8474 #15694813

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#8474

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
prime radical	C₂×C₁₃×#41	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

682 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 150 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)(14,15,17,21,18,20,26,28)(16,22,23,29,24,19,25,27)(31,35,37,40)(36,44,45,43);(14,16,18,24)(15,19,20,22)(17,25,26,23)(21,29,28,27)(30,31)(32,36)(33,40)(34,37)(35,42)(38,43)(39,45)(41,44);(15,20)(17,26)(19,22)(23,25)(30,32,34,39)(31,36,37,45)(33,41,42,38)(35,43,40,44)

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, 1462);