C₂²×C₉×C₁₁×C₃₇ #28410798

order	14652
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian

C₂²×C₉×C₁₁×C₃₇

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₁₁×C₃₇
socle, prime radical	C₂²×C₃×C₁₁×C₃₇	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 61
transitive degree	μ_t(G) = 14652

A minimal faithful permutation representation — 2 generators on 61 points:

(1,2)(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);(3,4)

Conjugacy classes & character table

14652 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₄×C₉×C₁₁×C₃₇, C₂³×C₉×C₁₁×C₃₇
maximal normal subgroup of	C₂×C₄×C₉×C₁₁×C₃₇, C₂³×C₉×C₁₁×C₃₇
maximal quotient of	C₂×C₄×C₉×C₁₁×C₃₇, C₂³×C₉×C₁₁×C₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14652, 13);

C22×C9×C11×C37 #28410798