C₂×#872 #5472

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) order 24576
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

Fitting	C₂×C₃×C₄² ⋊ C₂
Sylow	C₃ ⋊ C₂×#117

330 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 4 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1031);