C₂²×C₅²×C₇ #10622017

order	700
nilpotency class	1
isoclinism	isoclinic class of C₁
automorphism	Aut(G) order 17280
homology	Abelianization (H₁) = G · Schur multiplier (H₂) = C₂×C₅

Aliases

abelian	C₂²×C₅²×C₇
multiplicative	(ℤ/781)ˣ, (ℤ/1562)ˣ

80 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 700

A minimal faithful permutation representation — 2 generators on 21 points:

(1,2)(5,6,7,8,9)(15,16,17,18,19,20,21);(3,4)(10,11,12,13,14)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(700, 36);