C₂²×C₃×C₇×C₁₇² #37566216

order	24276
nilpotency class	1
automorphism	?
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₁₇

Aliases

abelian	C₂²×C₃×C₇×C₁₇²
multiplicative	(ℤ/24617)ˣ, (ℤ/49234)ˣ

400 conjugacy classes of subgroups.

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 24276

A minimal faithful permutation representation — 2 generators on 48 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);(3,4)(32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48)

24276 conjugacy classes. The character table is too large to display.

automorphism group of	C₁₀₃×C₂₃₉
outer automorphism group of	C₁₀₃×C₂₃₉

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24276, 69);