C₅×C₁₁×C₁₃⋊C₃ #14524095

order	2145
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₅×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₁×C₁₃⋊C₃
unambiguous semidirect product	C₁₃⋊(C₃×C₅×C₁₁)
unambiguous semidirect product	(C₅×C₁₃)⋊(C₃×C₁₁)
unambiguous semidirect product	(C₅×C₁₁×C₁₃)⋊C₃

	subgroup	G/H
center, hypercenter	C₅×C₁₁	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₃×C₅×C₁₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₃	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₅×C₁₁

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 715

A minimal faithful permutation representation — 2 generators on 29 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16)(18,19,21)(20,23,26)(22,25,24)(27,29,28);(17,18,20,19,22,26,23,27,29,21,24,28,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2145, 3);