D₁₂₄₈₃ #38735702

order	24966
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₄₈₃
unambiguous semidirect product	C₉⋊D₁₃₈₇
unambiguous semidirect product	C₁₉⋊D₆₅₇
unambiguous semidirect product	C₇₃⋊D₁₇₁

Splittings

Fitting, derived, Hall	C₉×C₁₉×C₇₃ ⋊ C₂
Hall	C₁₉×C₇₃ ⋊ D₉
Hall	C₉×C₇₃ ⋊ D₁₉
Hall	C₉×C₁₉ ⋊ D₇₃
Sylow	C₇₃ ⋊ D₁₇₁
Sylow	C₁₉ ⋊ D₆₅₇
Sylow	C₉ ⋊ D₁₃₈₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₉×C₁₉×C₇₃	C₂
Frattini	C₃	D₄₁₆₁
socle	C₃×C₁₉×C₇₃	D₃
LCS	G ▷ C₉×C₁₉×C₇₃
UCS	C₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 12483

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

Polycyclic presentation:

2,3,19,73,3|b^3=e^2,b^a=b^2e,c^a=c^18,d^a=d^72,e^a=e^2

Conjugacy classes & character table

6243 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24966, 12);

D12483 #38735702