Dic₈₉₆₁ #49089453

order	35844
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

dicyclic	Dic₈₉₆₁
unambiguous semidirect product	C₃⋊Dic₂₉₈₇
unambiguous semidirect product	C₁₀₃⋊Dic₈₇

Splittings

derived, Hall	C₃×C₂₉×C₁₀₃ ⋊ C₄
Hall	C₂₉×C₁₀₃ ⋊ Dic₃
Hall	C₃×C₁₀₃ ⋊ Dic₂₉
Sylow	C₁₀₃ ⋊ Dic₈₇
Hall	C₃×C₂₉ ⋊ Dic₁₀₃
Sylow	C₂₉ ⋊ Dic₃₀₉
Sylow	C₃ ⋊ Dic₂₉₈₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₈₉₆₁
commutator, hypocenter	C₃×C₂₉×C₁₀₃	C₄
Fitting, socle, prime radical, cosocle	C₂×C₃×C₂₉×C₁₀₃	C₂
LCS	G ▷ C₃×C₂₉×C₁₀₃
UCS	C₁ ◁ C₂

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 139
transitive degree	μ_t(G) = 35844

A minimal faithful permutation representation — 2 generators on 139 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)(37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139);(1,3,2,4)(6,7)(9,36)(10,35)(11,34)(12,33)(13,32)(14,31)(15,30)(16,29)(17,28)(18,27)(19,26)(20,25)(21,24)(22,23)(38,139)(39,138)(40,137)(41,136)(42,135)(43,134)(44,133)(45,132)(46,131)(47,130)(48,129)(49,128)(50,127)(51,126)(52,125)(53,124)(54,123)(55,122)(56,121)(57,120)(58,119)(59,118)(60,117)(61,116)(62,115)(63,114)(64,113)(65,112)(66,111)(67,110)(68,109)(69,108)(70,107)(71,106)(72,105)(73,104)(74,103)(75,102)(76,101)(77,100)(78,99)(79,98)(80,97)(81,96)(82,95)(83,94)(84,93)(85,92)(86,91)(87,90)(88,89)

Polycyclic presentation:

2,3,29,103,2|a^2=e,b^a=b^2,c^a=c^28,d^a=d^102

Conjugacy classes & character table

8964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35844, 9);

Dic8961 #49089453