D₁₈₀₃₁ #49115203

order	36062
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₈₀₃₁
unambiguous semidirect product	C₁₃⋊D₁₃₈₇
unambiguous semidirect product	C₁₉⋊D₉₄₉
unambiguous semidirect product	C₇₃⋊D₂₄₇

Splittings

Fitting, socle, derived, Hall	C₁₃×C₁₉×C₇₃ ⋊ C₂
Hall	C₁₉×C₇₃ ⋊ D₁₃
Hall	C₁₃×C₇₃ ⋊ D₁₉
Hall	C₁₃×C₁₉ ⋊ D₇₃
Sylow	C₇₃ ⋊ D₂₄₇
Sylow	C₁₉ ⋊ D₉₄₉
Sylow	C₁₃ ⋊ D₁₃₈₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₉×C₇₃	C₂
LCS	G ▷ C₁₃×C₁₉×C₇₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 18031

A minimal faithful permutation representation — 2 generators on 105 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(34,105)(35,104)(36,103)(37,102)(38,101)(39,100)(40,99)(41,98)(42,97)(43,96)(44,95)(45,94)(46,93)(47,92)(48,91)(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Polycyclic presentation:

2,13,19,73|b^a=b^12,c^a=c^18,d^a=d^72

Conjugacy classes & character table

9017 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36062, 8);

D18031 #49115203