C₂×#6377 #89693

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³

Aliases

146 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 3 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 455);