C₁₃×#11994 #15698333

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11994
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11994

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1558
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	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

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

normal subgroups only

This group has 258 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)(14,15,17,22,31,23,41,40,19,24,30,39,18,21,32,37)(16,25,27,38,33,36,29,44,26,42,43,45,28,20,34,35);(14,16,19,26)(15,20)(17,29,30,34)(18,33,31,28)(21,25)(22,38)(23,42)(24,36)(27,32,43,41)(35,40)(37,44)(39,45);(17,30)(22,39)(27,43)(29,34)(32,41)(35,44)(37,40)(38,45)

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, 4982);