C₁₇×D₆₃ #14523875

order	2142
isoclinism	isoclinic class of D₆₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₆₃
unambiguous semidirect product	C₇⋊(C₁₇×D₉)
unambiguous semidirect product	C₉⋊(D₇×C₁₇)

	subgroup	G/H
center, hypercenter	C₁₇	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂×C₁₇
Frattini	C₃	C₁₇×D₂₁
Fitting	C₇×C₉×C₁₇	C₂
socle	C₃×C₇×C₁₇	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₁₇

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1071

A minimal faithful permutation representation — 2 generators on 33 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)(27,28,29,30,31,32,33);(19,26)(20,25)(21,24)(22,23)(28,33)(29,32)(30,31)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2142, 11);