C₂×C₃⋊#622 #88992

order	432
isoclinism	isoclinic class of C₃⋊#157
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₂×C₃⋊#622
unambiguous semidirect product	(C₂×C₃)⋊#622

C₃³ ⋊ C₂×C₈

96 conjugacy classes of subgroups.

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 19 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 639);