C₂×C₉×C₂₉×C₄₃ #36376287

order	22446
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₁

Aliases

cyclic	C₂₂₄₄₆
abelian	C₂×C₉×C₂₉×C₄₃
multiplicative	(ℤ/22447)ˣ, (ℤ/44894)ˣ

Subgroups

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂×C₃×C₂₉×C₄₃
socle, prime radical	C₂×C₃×C₂₉×C₄₃	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 83
transitive degree	μ_t(G) = 22446

A minimal faithful permutation representation — 1 generator on 83 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)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83)

Conjugacy classes & character table

22446 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₂₂₄₄₇
outer automorphism group of	C₂₂₄₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22446, 1);

C2×C9×C29×C43 #36376287