C₂×Dic₇⋊C₈ #89871

order	448
isoclinism	isoclinic class of Dic₁₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂³

Aliases

138 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:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 633);