C₂×C₃×C₅×C₁₇×C₃₇ #34038260

order	18870
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₁₈₈₇₀
abelian	C₂×C₃×C₅×C₁₇×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) = 64
transitive degree	μ_t(G) = 18870

A minimal faithful permutation representation — 1 generator on 64 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)

Conjugacy classes & character table

18870 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃×C₅×C₁₇×Dic₃₇, C₃×C₅×C₃₇×Dic₁₇, C₃×C₅×Dic₆₂₉, …
socle of	C₃×C₄×C₅×C₁₇×C₃₇, C₃×C₅×C₁₇×Dic₃₇, C₃×C₅×C₃₇×Dic₁₇, …
maximal subgroup of	C₃×C₄×C₅×C₁₇×C₃₇, C₃×C₅×C₁₇×Dic₃₇, C₃×C₅×C₃₇×Dic₁₇, …
maximal normal subgroup of	C₃×C₄×C₅×C₁₇×C₃₇, C₃×C₅×C₁₇×Dic₃₇, C₃×C₅×C₃₇×Dic₁₇, …
maximal quotient of	C₃×C₄×C₅×C₁₇×C₃₇, C₂²×C₃×C₅×C₁₇×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 1);

C2×C3×C5×C17×C37 #34038260