C₂×#4557 #71991

order	384
isoclinism	isoclinic class of #4466
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂³×C₄

Aliases

404 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 4567);