C₂³×C₁₇×C₃₂ #16891715

order	4352
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 2752512
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂⁶

Aliases

abelian

C₂³×C₁₇×C₃₂

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂⁴×C₁₇
socle, prime radical	C₂⁴×C₁₇	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

542 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 4 generators on 55 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)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(33,34);(35,36);(37,38)

Conjugacy classes & character table

4352 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂³×C₁₇×C₆₄, C₂⁴×C₁₇×C₃₂, C₂²×C₄×C₁₇×C₃₂, …
maximal normal subgroup of	C₂³×C₁₇×C₆₄, C₂⁴×C₁₇×C₃₂, C₂²×C₄×C₁₇×C₃₂, …
maximal quotient of	C₂³×C₁₇×C₆₄, C₂⁴×C₁₇×C₃₂, C₂²×C₄×C₁₇×C₃₂, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26959);

C23×C17×C32 #16891715