C₂×#5727 #86212

order	384
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

Fitting	C₂×C₃×C₄⋊Q₈ ⋊ C₂
Sylow	C₃ ⋊ C₂×D₄×Q₈

1568 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 5 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18788);