C₂×#5139 #83778

order	384
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶

Aliases

Fitting	C₂²×C₃×M₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂×#421

772 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 96

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 16354);