C₂²×#798 #81999

order	384
isoclinism	isoclinic class of Dic₆
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁵

Aliases

Fitting	C₂²×C₃×C₁₆ ⋊ C₂
Sylow	C₃ ⋊ C₂²×M₃₂

400 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 192

A minimal faithful permutation representation — 4 generators on 23 points:

(5,6,7)(8,9,10,14,11,15,16,21,12,13,17,19,18,20,22,23);(1,2)(3,4)(6,7)(9,13)(14,19)(15,20)(21,23);(3,4);(1,2)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 14575);