D₁₈₆₉₃ #49153268

order	37386
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₈₆₉₃
unambiguous semidirect product	C₉⋊D₂₀₇₇
unambiguous semidirect product	C₃₁⋊D₆₀₃
unambiguous semidirect product	C₆₇⋊D₂₇₉

Splittings

Fitting, derived, Hall	C₉×C₃₁×C₆₇ ⋊ C₂
Hall	C₃₁×C₆₇ ⋊ D₉
Hall	C₉×C₆₇ ⋊ D₃₁
Hall	C₉×C₃₁ ⋊ D₆₇
Sylow	C₆₇ ⋊ D₂₇₉
Sylow	C₃₁ ⋊ D₆₀₃
Sylow	C₉ ⋊ D₂₀₇₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₃₁×C₆₇	C₂
Frattini	C₃	D₆₂₃₁
socle	C₃×C₃₁×C₆₇	D₃
LCS	G ▷ C₉×C₃₁×C₆₇
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 107
transitive degree	μ_t(G) = 18693

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

Polycyclic presentation:

2,3,31,67,3|b^3=e^2,b^a=b^2e,c^a=c^30,d^a=d^66,e^a=e^2

Conjugacy classes & character table

9348 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37386, 12);

D18693 #49153268