C₂²×C₃×C₂₉×C₇₃ #38761925

order	25404
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₂₉×C₇₃
multiplicative	(ℤ/25901)ˣ, (ℤ/38109)ˣ, (ℤ/50812)ˣ, (ℤ/51802)ˣ, (ℤ/76218)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) = 109
transitive degree	μ_t(G) = 25404

A minimal faithful permutation representation — 2 generators on 109 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109);(3,4)

Conjugacy classes & character table

25404 conjugacy classes. The character table is too large to display.

Relationships

automorphism group of	C₅₉×C₄₃₉
outer automorphism group of	C₅₉×C₄₃₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25404, 13);

C22×C3×C29×C73 #38761925