C₂²×C₉×C₂₃×C₂₉ #37562147

order	24012
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₉×C₂₃×C₂₉
multiplicative	(ℤ/24581)ˣ, (ℤ/36021)ˣ, (ℤ/48028)ˣ, (ℤ/49162)ˣ, (ℤ/72042)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂²×C₃×C₂₃×C₂₉
socle, prime radical	C₂²×C₃×C₂₃×C₂₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 65
transitive degree	μ_t(G) = 24012

A minimal faithful permutation representation — 2 generators on 65 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65);(3,4)

Conjugacy classes & character table

24012 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₄₇×C₅₂₃
outer automorphism group of	C₄₇×C₅₂₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24012, 9);

C22×C9×C23×C29 #37562147