Dic₂₈₆₇ #26039726

order	11468
automorphism	Aut(G) order 15825840
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₂₈₆₇
unambiguous semidirect product	C₄₇⋊Dic₆₁

Splittings

derived, Hall	C₄₇×C₆₁ ⋊ C₄
Sylow	C₆₁ ⋊ Dic₄₇
Sylow	C₄₇ ⋊ Dic₆₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₂₈₆₇
commutator, hypocenter	C₄₇×C₆₁	C₄
Fitting, socle, prime radical, cosocle	C₂×C₄₇×C₆₁	C₂
LCS	G ▷ C₄₇×C₆₁
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 112
transitive degree	μ_t(G) = 11468

A minimal faithful permutation representation — 2 generators on 112 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)(52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112);(1,3,2,4)(6,51)(7,50)(8,49)(9,48)(10,47)(11,46)(12,45)(13,44)(14,43)(15,42)(16,41)(17,40)(18,39)(19,38)(20,37)(21,36)(22,35)(23,34)(24,33)(25,32)(26,31)(27,30)(28,29)(53,112)(54,111)(55,110)(56,109)(57,108)(58,107)(59,106)(60,105)(61,104)(62,103)(63,102)(64,101)(65,100)(66,99)(67,98)(68,97)(69,96)(70,95)(71,94)(72,93)(73,92)(74,91)(75,90)(76,89)(77,88)(78,87)(79,86)(80,85)(81,84)(82,83)

Polycyclic presentation:

2,47,61,2|a^2=d,b^a=b^46,c^a=c^60

Conjugacy classes & character table

2870 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×Dic₂₈₆₇, Dic₈₆₀₁, C₄₇⋊(Dic₆₁⋊C₃), …
maximal normal subgroup of	C₃×Dic₂₈₆₇, C₄₇⋊(Dic₆₁⋊C₃), Dic₅₇₃₄
maximal quotient of	C₃×Dic₂₈₆₇, Dic₈₆₀₁, Dic₁₄₃₃₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11468, 4);

Dic2867 #26039726