Dic₄₉₂₉ #34089308

order	19716
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₄₉₂₉
unambiguous semidirect product	C₃⋊Dic₁₆₄₃
unambiguous semidirect product	C₃₁⋊Dic₁₅₉

Splittings

derived, Hall	C₃×C₃₁×C₅₃ ⋊ C₄
Hall	C₃₁×C₅₃ ⋊ Dic₃
Hall	C₃×C₅₃ ⋊ Dic₃₁
Hall	C₃×C₃₁ ⋊ Dic₅₃
Sylow	C₅₃ ⋊ Dic₉₃
Sylow	C₃₁ ⋊ Dic₁₅₉
Sylow	C₃ ⋊ Dic₁₆₄₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₄₉₂₉
commutator, hypocenter	C₃×C₃₁×C₅₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₃₁×C₅₃	C₂
LCS	G ▷ C₃×C₃₁×C₅₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 19716

A minimal faithful permutation representation — 2 generators on 91 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);(1,3,2,4)(6,7)(9,38)(10,37)(11,36)(12,35)(13,34)(14,33)(15,32)(16,31)(17,30)(18,29)(19,28)(20,27)(21,26)(22,25)(23,24)(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:

2,3,31,53,2|a^2=e,b^a=b^2,c^a=c^30,d^a=d^52

Conjugacy classes & character table

4932 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₉₈₅₈, Dic₁₄₇₈₇
maximal normal subgroup of	Dic₉₈₅₈
maximal quotient of	Dic₁₄₇₈₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19716, 9);

Dic4929 #34089308