C₇×C₁₇×D₉ #14523873

order	2142
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₇×D₉
unambiguous semidirect product	C₉⋊(C₂×C₇×C₁₇)

	subgroup	G/H
center, hypercenter	C₇×C₁₇	D₉
commutator, cosocle, hypocenter	C₉	C₂×C₇×C₁₇
Frattini	C₃	D₃×C₇×C₁₇
Fitting	C₇×C₉×C₁₇	C₂
socle	C₃×C₇×C₁₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₇×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);(26,33)(27,32)(28,31)(29,30)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2142, 9);