C₂²×C₃×C₇×C₁₃×C₂₃ #38737330

order	25116
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂

Aliases

abelian	C₂²×C₃×C₇×C₁₃×C₂₃
multiplicative	(ℤ/25709)ˣ, (ℤ/25757)ˣ, (ℤ/29351)ˣ, (ℤ/51418)ˣ, (ℤ/51514)ˣ, (ℤ/58702)ˣ

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 50
transitive degree	μ_t(G) = 25116

A minimal faithful permutation representation — 2 generators on 50 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);(3,4)

25116 conjugacy classes. The character table is too large to display.

automorphism group of	C₄₇×C₅₄₇, C₄₃×C₅₉₉
outer automorphism group of	C₄₇×C₅₄₇, C₄₃×C₅₉₉

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 49);