C₂²×#1088 #88896

order	432
isoclinism	isoclinic class of #1088
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

Fitting	C₂²×H(3,𝔽₃) ⋊ C₄
derived, Sylow	H(3,𝔽₃) ⋊ C₂²×C₄

145 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 72

A minimal faithful permutation representation — 3 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 543);