C₂²×(C₂×D₃)⋊C₄ #5787

order	192
isoclinism	isoclinic class of Dic₆
automorphism	Aut(G) order 147456
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

Fitting	C₂³×C₃×C₄ ⋊ C₂
Sylow	C₃ ⋊ C₂²×C₂²⋊C₄

674 conjugacy classes of subgroups.

minimal degree	μ(G) = 15
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 4 generators on 15 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(192, 1346);