C₅×C₁₃×D₃₃ #16864249

order	4290
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₃×D₃₃
unambiguous semidirect product	C₃⋊(C₅×C₁₃×D₁₁)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₅×C₁₃

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 2145

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18)(19,20,21)(22,23,24,25,26,27,28,29,30,31,32);(20,21)(23,32)(24,31)(25,30)(26,29)(27,28)

1170 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4290, 14);