C₄×C₉×C₂₉×C₃₁ #44569015

order	32364
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₂₃₆₄
abelian	C₄×C₉×C₂₉×C₃₁

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₂₉×C₃₁
socle, prime radical	C₂×C₃×C₂₉×C₃₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 73
transitive degree	μ_t(G) = 32364

A minimal faithful permutation representation — 1 generator on 73 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)

Conjugacy classes & character table

32364 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₆₁₈₂, D₃₂₃₆₄
maximal subgroup of	Dic₁₆₁₈₂, D₃₂₃₆₄
maximal normal subgroup of	Dic₁₆₁₈₂, D₃₂₃₆₄

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32364, 1);

C4×C9×C29×C31 #44569015