D₃×#622 #88923

order	432
isoclinism	isoclinic class of D₃×#157
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂×C₃

Aliases

C₃³ ⋊ C₂×C₈

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×#157
commutator, hypocenter	C₃³	C₂×C₈
Fitting, socle	C₂×C₃³	C₂×C₄
prime radical	C₂×C₃²×D₃	C₄
cosocle	C₃×C₃⋊Dic₃	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₂

88 conjugacy classes of subgroups.

minimal degree	μ(G) = 17
transitive degree	μ_t(G) = 48

A minimal faithful permutation representation — 2 generators on 17 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(432, 570);