C₁₇×C₃⋊D₃₃ #16809882

order	3366
isoclinism	isoclinic class of C₃⋊D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₇×C₃⋊D₃₃
unambiguous semidirect product	C₃⋊(C₁₇×D₃₃)
unambiguous semidirect product	C₁₁⋊(C₁₇×C₃⋊D₃)

	subgroup	G/H
center, hypercenter	C₁₇	C₃⋊D₃₃
commutator, cosocle, hypocenter	C₃²×C₁₁	C₂×C₁₇
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₁₇	C₂
LCS	G ▷ C₃²×C₁₁
UCS	C₁ ◁ C₁₇

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 34
transitive degree	μ_t(G) = 1683

A minimal faithful permutation representation — 3 generators on 34 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3366, 19);