C₁₃×#11916 #15698255

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11915
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11916

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1533
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	#97	C₂³×C₁₃
prime radical	C₂³×C₁₃	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

274 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 90 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)(14,15,17,23,18,24,31,42,19,21,30,38,33,22,39,40)(16,25,26,43,27,20,34,36,28,37,44,41,32,35,29,45);(14,16,19,28)(15,20,21,35)(17,29,30,34)(18,32,33,27)(22,37,24,25)(23,41,38,43)(26,31,44,39)(36,40,45,42);(15,21)(17,30)(20,35)(22,24)(25,37)(26,44)(29,34)(31,39)

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, 4904);