C₄×#226 #5387

order	192
isoclinism	isoclinic class of #226
automorphism	Aut(G) = C₂⁴×S₄ (order 384) · Inn(G) = S₄ · Out(G) = C₂⁴
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

70 conjugacy classes of subgroups.

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 2 generators on 20 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 946);