C₂²×C₅²×C₁₃×C₁₉ #37590804

order	24700
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

abelian	C₂²×C₅²×C₁₃×C₁₉
multiplicative	(ℤ/25021)ˣ, (ℤ/50042)ˣ

160 conjugacy classes of subgroups.

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 24700

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2)(5,6,7,8,9)(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);(3,4)(10,11,12,13,14)

24700 conjugacy classes. The character table is too large to display.

automorphism group of	C₁₃₁×C₁₉₁
outer automorphism group of	C₁₃₁×C₁₉₁

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24700, 48);