C₂²×C₃²×C₁₁×C₆₁ #37563503

order	24156
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₃

Aliases

abelian	C₂²×C₃²×C₁₁×C₆₁
multiplicative	(ℤ/24589)ˣ, (ℤ/28189)ˣ, (ℤ/36243)ˣ, (ℤ/49178)ˣ, (ℤ/56378)ˣ, (ℤ/72486)ˣ

Subgroups

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

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 24156

A minimal faithful permutation representation — 2 generators on 82 points:

(1,2)(5,6,7)(11,12,13,14,15,16,17,18,19,20,21)(22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82);(3,4)(8,9,10)

Conjugacy classes & character table

24156 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₆₇×C₃₆₇
outer automorphism group of	C₆₇×C₃₆₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24156, 61);

C22×C32×C11×C61 #37563503