D₁₇₉₇₃ #49090697

order	35946
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₇₉₇₃
unambiguous semidirect product	C₉⋊D₁₉₉₇
unambiguous semidirect product	C₁₉₉₇⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₉₉₇ ⋊ C₂
Sylow	C₁₉₉₇ ⋊ D₉
Sylow	C₉ ⋊ D₁₉₉₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₉₉₇	C₂
Frattini	C₃	D₅₉₉₁
socle	C₃×C₁₉₉₇	D₃
LCS	G ▷ C₉×C₁₉₉₇
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 2006
transitive degree	μ_t(G) = 17973

A minimal faithful permutation representation — 2 generators on 2006 points:

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Polycyclic presentation:

2,3,1997,3|b^3=d^2,b^a=b^2d,c^a=c^1996,d^a=d^2

Conjugacy classes & character table

8988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35946, 4);

D17973 #49090697