C₁₃×#11993 #15698332

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11992
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#11993

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1555
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#532	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

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

normal subgroups only

This group has 360 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) = 416

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

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

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4981);