Dic₁₄₈₃₉ #72292126

order	59356
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic

Dic₁₄₈₃₉

Splittings

derived, Hall	C₁₁×C₁₉×C₇₁ ⋊ C₄
Hall	C₁₉×C₇₁ ⋊ Dic₁₁
Hall	C₁₁×C₇₁ ⋊ Dic₁₉
Hall	C₁₁×C₁₉ ⋊ Dic₇₁
Sylow	C₇₁ ⋊ Dic₂₀₉
Sylow	C₁₉ ⋊ Dic₇₈₁
Sylow	C₁₁ ⋊ Dic₁₃₄₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₄₈₃₉
commutator, hypocenter	C₁₁×C₁₉×C₇₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₁₁×C₁₉×C₇₁	C₂
LCS	G ▷ C₁₁×C₁₉×C₇₁
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 105
transitive degree	μ_t(G) = 59356

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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(36,105)(37,104)(38,103)(39,102)(40,101)(41,100)(42,99)(43,98)(44,97)(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Polycyclic presentation:

2^2,11,19,71|a^2=b,c^a=c^10,d^a=d^18,e^a=e^70

Conjugacy classes & character table

14842 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its polycyclic presentation:

gap> F := FreeGroup(IsSyllableWordsFamily, "a", "b", "c", "d", "e");;
gap> coll := SingleCollector(F, [2, 2, 11, 19, 71]);;
gap> SetPower(coll, 1, F.2);;
gap> SetConjugate(coll, 3, 1, F.3^10);;
gap> SetConjugate(coll, 4, 1, F.4^18);;
gap> SetConjugate(coll, 5, 1, F.5^70);;
gap> UpdatePolycyclicCollector(coll);;
gap> G := GroupByRws(coll);

Dic14839 #72292126