C₂×C₃²×C₅²×C₃₇ #30659263

order	16650
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₃×C₅

Aliases

abelian

C₂×C₃²×C₅²×C₃₇

Subgroups

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

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 16650

A minimal faithful permutation representation — 2 generators on 55 points:

(1,2)(3,4,5)(9,10,11,12,13)(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);(6,7,8)(14,15,16,17,18)

Conjugacy classes & character table

16650 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup of	C₃⋊(C₃⋊#16814867), C₃₇×C₃⋊(C₃⋊#1039), C₅×C₃⋊Dic₅₅₅, …
socle of	C₃²×C₄×C₅²×C₃₇, C₃⋊(C₃⋊#16814867), C₃₇×C₃⋊(C₃⋊#1039), …
maximal subgroup of	C₃²×C₄×C₅²×C₃₇, C₃⋊(C₃⋊#16814867), C₃₇×C₃⋊(C₃⋊#1039), …
maximal normal subgroup of	C₃²×C₄×C₅²×C₃₇, C₃⋊(C₃⋊#16814867), C₃₇×C₃⋊(C₃⋊#1039), …
maximal quotient of	C₃²×C₄×C₅²×C₃₇, C₂²×C₃²×C₅²×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16650, 65);

C2×C32×C52×C37 #30659263