C₂×C₁₃×#1356 #15698249

order	3328
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂×C₁₃×#1356

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#329
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	#97	C₂³×C₁₃
prime radical	C₂³×C₁₃	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₁₃×#97 ◁ G

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

normal subgroups only

This group has 314 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) = 47
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 47 points:

(1,2)(35,36,37,38,39,40,41,42,43,44,45,46,47);(3,4,6,11,7,12,20,30,8,13,19,31,22,10,27,28)(5,14,15,32,16,9,23,24,17,25,33,29,21,26,18,34);(3,5,8,17)(4,9,13,26)(6,18,19,23)(7,21,22,16)(10,25,12,14)(11,29,31,32)(15,20,33,27)(24,28,34,30)

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, 4898);