D₁₁₄₈₁ #37525822

order	22962
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₄₈₁
unambiguous semidirect product	C₃⋊D₃₈₂₇
unambiguous semidirect product	C₄₃⋊D₂₆₇
unambiguous semidirect product	C₈₉⋊D₁₂₉

Splittings

Fitting, socle, derived, Hall	C₃×C₄₃×C₈₉ ⋊ C₂
Hall	C₄₃×C₈₉ ⋊ D₃
Hall	C₃×C₈₉ ⋊ D₄₃
Hall	C₃×C₄₃ ⋊ D₈₉
Sylow	C₈₉ ⋊ D₁₂₉
Sylow	C₄₃ ⋊ D₂₆₇
Sylow	C₃ ⋊ D₃₈₂₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₄₃×C₈₉	C₂
LCS	G ▷ C₃×C₄₃×C₈₉
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 135
transitive degree	μ_t(G) = 11481

A minimal faithful permutation representation — 2 generators on 135 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);(2,3)(5,46)(6,45)(7,44)(8,43)(9,42)(10,41)(11,40)(12,39)(13,38)(14,37)(15,36)(16,35)(17,34)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)(48,135)(49,134)(50,133)(51,132)(52,131)(53,130)(54,129)(55,128)(56,127)(57,126)(58,125)(59,124)(60,123)(61,122)(62,121)(63,120)(64,119)(65,118)(66,117)(67,116)(68,115)(69,114)(70,113)(71,112)(72,111)(73,110)(74,109)(75,108)(76,107)(77,106)(78,105)(79,104)(80,103)(81,102)(82,101)(83,100)(84,99)(85,98)(86,97)(87,96)(88,95)(89,94)(90,93)(91,92)

Polycyclic presentation:

2,3,43,89|b^a=b^2,c^a=c^42,d^a=d^88

Conjugacy classes & character table

5742 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22962, 9);

D11481 #37525822