C₂×#5728 #86199

order	384
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸

Aliases

Fitting	C₂×C₃×C₄⋊Q₈ ⋊ C₂
Sylow	C₃ ⋊ C₂×#533

1168 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 5 generators on 21 points:

(1,2)(3,4,5)(6,8,9,13)(7,10,11,12)(14,16)(15,18)(17,20)(19,21);(6,7,9,11)(8,12,13,10);(14,15,17,19)(16,21,20,18);(4,5)(16,20)(18,21);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18775);