C₂²×C₁₁²×C₄₃ #35209557

order	20812
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₁₁

Aliases

abelian	C₂²×C₁₁²×C₄₃
multiplicative	(ℤ/21781)ˣ, (ℤ/43562)ˣ

Subgroups

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

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 69
transitive degree	μ_t(G) = 20812

A minimal faithful permutation representation — 2 generators on 69 points:

(1,2)(5,6,7,8,9,10,11,12,13,14,15)(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);(3,4)(16,17,18,19,20,21,22,23,24,25,26)

Conjugacy classes & character table

20812 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₂₃×C₉₄₇
outer automorphism group of	C₂₃×C₉₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20812, 16);

C22×C112×C43 #35209557