Dic₃₉₅₃ #30629060

order	15812
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₃₉₅₃
unambiguous semidirect product	C₅₉⋊Dic₆₇
unambiguous semidirect product	C₆₇⋊Dic₅₉

Splittings

derived, Hall	C₅₉×C₆₇ ⋊ C₄
Sylow	C₆₇ ⋊ Dic₅₉
Sylow	C₅₉ ⋊ Dic₆₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃₉₅₃
commutator, hypocenter	C₅₉×C₆₇	C₄
Fitting, socle, prime radical, cosocle	C₂×C₅₉×C₆₇	C₂
LCS	G ▷ C₅₉×C₆₇
UCS	C₁ ◁ C₂

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 130
transitive degree	μ_t(G) = 15812

A minimal faithful permutation representation — 2 generators on 130 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)(64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130);(1,3,2,4)(6,63)(7,62)(8,61)(9,60)(10,59)(11,58)(12,57)(13,56)(14,55)(15,54)(16,53)(17,52)(18,51)(19,50)(20,49)(21,48)(22,47)(23,46)(24,45)(25,44)(26,43)(27,42)(28,41)(29,40)(30,39)(31,38)(32,37)(33,36)(34,35)(65,130)(66,129)(67,128)(68,127)(69,126)(70,125)(71,124)(72,123)(73,122)(74,121)(75,120)(76,119)(77,118)(78,117)(79,116)(80,115)(81,114)(82,113)(83,112)(84,111)(85,110)(86,109)(87,108)(88,107)(89,106)(90,105)(91,104)(92,103)(93,102)(94,101)(95,100)(96,99)(97,98)

Polycyclic presentation:

2,59,67,2|a^2=d,b^a=b^58,c^a=c^66

Conjugacy classes & character table

3956 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	Dic₇₉₀₆
maximal normal subgroup of	Dic₇₉₀₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15812, 4);

Dic3953 #30629060