D₁₆₀₃₁ #44545456

order	32062
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₀₃₁
unambiguous semidirect product	C₁₇⋊D₉₄₃
unambiguous semidirect product	C₂₃⋊D₆₉₇
unambiguous semidirect product	C₄₁⋊D₃₉₁

Splittings

Fitting, socle, derived, Hall	C₁₇×C₂₃×C₄₁ ⋊ C₂
Hall	C₂₃×C₄₁ ⋊ D₁₇
Hall	C₁₇×C₄₁ ⋊ D₂₃
Hall	C₁₇×C₂₃ ⋊ D₄₁
Sylow	C₄₁ ⋊ D₃₉₁
Sylow	C₂₃ ⋊ D₆₉₇
Sylow	C₁₇ ⋊ D₉₄₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₇×C₂₃×C₄₁	C₂
LCS	G ▷ C₁₇×C₂₃×C₄₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 16031

A minimal faithful permutation representation — 2 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81);(2,17)(3,16)(4,15)(5,14)(6,13)(7,12)(8,11)(9,10)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)

Polycyclic presentation:

2,17,23,41|b^a=b^16,c^a=c^22,d^a=d^40

Conjugacy classes & character table

8017 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₆₀₃₁
maximal normal subgroup of	C₂×D₁₆₀₃₁
maximal quotient of	Dic₁₆₀₃₁, C₂×D₁₆₀₃₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32062, 8);

D16031 #44545456