C₄×#947 #82452

order	384
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

Fitting	C₂×C₃×C₄×Q₈ ⋊ C₂
Sylow	C₃ ⋊ C₄×#124

652 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)(9,11)(12,14,15,19)(13,17,16,18);(12,13,15,16)(14,18,19,17);(2,3)(8,9)(10,11)(13,16)(17,18);(4,5,6,7)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 15028);