C₄×#894 #73757

order	384
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₃×C₄×C₄⋊C₄ ⋊ C₂
Sylow	C₃ ⋊ C₄×#123

688 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 4 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 6333);