C₄×C₁₁×C₁₇×C₄₃ #44565478

order	32164
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₁₆₄
abelian	C₄×C₁₁×C₁₇×C₄₃

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₁₁×C₁₇×C₄₃
socle, prime radical	C₂×C₁₁×C₁₇×C₄₃	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 32164

A minimal faithful permutation representation — 1 generator on 75 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75)

Conjugacy classes & character table

32164 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₆₀₈₂, D₃₂₁₆₄
maximal subgroup of	Dic₁₆₀₈₂, D₃₂₁₆₄
maximal normal subgroup of	Dic₁₆₀₈₂, D₃₂₁₆₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32164, 1);

C4×C11×C17×C43 #44565478