C₂×C₃×C₁₁×C₁₃×C₃₇ #44540788

order	31746
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₃₁₇₄₆
abelian	C₂×C₃×C₁₁×C₁₃×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 31746

A minimal faithful permutation representation — 1 generator on 66 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)

Conjugacy classes & character table

31746 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	Dic₁₅₈₇₃, C₂×D₁₅₈₇₃
socle of	Dic₁₅₈₇₃, C₂×D₁₅₈₇₃
maximal subgroup of	Dic₁₅₈₇₃, C₂×D₁₅₈₇₃
maximal normal subgroup of	Dic₁₅₈₇₃, C₂×D₁₅₈₇₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31746, 1);

C2×C3×C11×C13×C37 #44540788