C₅×C₃⋊D₃×C₃₁ #14584085

order	2790
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₃₁ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₃⋊D₃×C₃₁
unambiguous semidirect product	C₃⋊(C₅×D₃×C₃₁)

	subgroup	G/H
center, hypercenter	C₅×C₃₁	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₃₁	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₃₁

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 42
transitive degree	μ_t(G) = 1395

A minimal faithful permutation representation — 3 generators on 42 points:

(1,2,3,4,5)(7,8)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42);(9,10,11);(6,7,8)

930 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2790, 45);