C₂²×C₅×C₂₃×C₄₃ #34089910

order	19780
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₅×C₂₃×C₄₃
multiplicative	(ℤ/20257)ˣ, (ℤ/21769)ˣ, (ℤ/40514)ˣ, (ℤ/43538)ˣ

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 75
transitive degree	μ_t(G) = 19780

A minimal faithful permutation representation — 2 generators on 75 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75);(3,4)

Conjugacy classes & character table

19780 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₄₇×C₄₃₁, C₁₁×C₁₉₇₉
outer automorphism group of	C₄₇×C₄₃₁, C₁₁×C₁₉₇₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19780, 9);

C22×C5×C23×C43 #34089910