C₂×#4455 #69722

order	384
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈ · Schur multiplier (H₂) = C₂²×C₄

Aliases

248 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 384

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 2298);