C₂³×C₁₃×C₃₂ #15720310

order	3328
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2064384
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian

C₂³×C₁₃×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂⁴×C₁₃
socle, prime radical	C₂⁴×C₁₃	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 4 generators on 51 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32)(39,40,41,42,43,44,45,46,47,48,49,50,51);(33,34);(35,36);(37,38)

Conjugacy classes & character table

3328 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₁₃×C₆₄, C₂⁴×C₁₃×C₃₂, C₂²×C₄×C₁₃×C₃₂, …
maximal normal subgroup of	C₂³×C₁₃×C₆₄, C₂⁴×C₁₃×C₃₂, C₂²×C₄×C₁₃×C₃₂, …
maximal quotient of	C₂³×C₁₃×C₆₄, C₂⁴×C₁₃×C₃₂, C₂²×C₄×C₁₃×C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 26959);

C23×C13×C32 #15720310