D₁₉₀₅₃ #49185498

order	38106
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₉₀₅₃
unambiguous semidirect product	C₉⋊D₂₁₁₇
unambiguous semidirect product	C₂₉⋊D₆₅₇
unambiguous semidirect product	C₇₃⋊D₂₆₁

Splittings

Fitting, derived, Hall	C₉×C₂₉×C₇₃ ⋊ C₂
Hall	C₂₉×C₇₃ ⋊ D₉
Hall	C₉×C₇₃ ⋊ D₂₉
Hall	C₉×C₂₉ ⋊ D₇₃
Sylow	C₇₃ ⋊ D₂₆₁
Sylow	C₂₉ ⋊ D₆₅₇
Sylow	C₉ ⋊ D₂₁₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₂₉×C₇₃	C₂
Frattini	C₃	D₆₃₅₁
socle	C₃×C₂₉×C₇₃	D₃
LCS	G ▷ C₉×C₂₉×C₇₃
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 111
transitive degree	μ_t(G) = 19053

A minimal faithful permutation representation — 2 generators on 111 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)(39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111);(2,9)(3,8)(4,7)(5,6)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(40,111)(41,110)(42,109)(43,108)(44,107)(45,106)(46,105)(47,104)(48,103)(49,102)(50,101)(51,100)(52,99)(53,98)(54,97)(55,96)(56,95)(57,94)(58,93)(59,92)(60,91)(61,90)(62,89)(63,88)(64,87)(65,86)(66,85)(67,84)(68,83)(69,82)(70,81)(71,80)(72,79)(73,78)(74,77)(75,76)

Polycyclic presentation:

2,3,29,73,3|b^3=e^2,b^a=b^2e,c^a=c^28,d^a=d^72,e^a=e^2

Conjugacy classes & character table

9528 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38106, 9);

D19053 #49185498