D₁₆₁₀₁ #44567200

order	32202
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₁₀₁
unambiguous semidirect product	C₉⋊D₁₇₈₉
unambiguous semidirect product	C₁₇₈₉⋊D₉

Splittings

Fitting, derived, Hall	C₉×C₁₇₈₉ ⋊ C₂
Sylow	C₁₇₈₉ ⋊ D₉
Sylow	C₉ ⋊ D₁₇₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₇₈₉	C₂
Frattini	C₃	D₅₃₆₇
socle	C₃×C₁₇₈₉	D₃
LCS	G ▷ C₉×C₁₇₈₉
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1798
transitive degree	μ_t(G) = 16101

A minimal faithful permutation representation — 2 generators on 1798 points:

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Polycyclic presentation:

2,3,1789,3|b^3=d^2,b^a=b^2d,c^a=c^1788,d^a=d^2

Conjugacy classes & character table

8052 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₁₀₁
maximal normal subgroup of	C₂×D₁₆₁₀₁
maximal quotient of	Dic₁₆₁₀₁, C₂×D₁₆₁₀₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32202, 6);

D16101 #44567200