D₁₁₉₃₁ #37558790

order	23862
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₉₃₁
unambiguous semidirect product	C₃⋊D₃₉₇₇
unambiguous semidirect product	C₄₁⋊D₂₉₁
unambiguous semidirect product	C₉₇⋊D₁₂₃

Splittings

Fitting, socle, derived, Hall	C₃×C₄₁×C₉₇ ⋊ C₂
Hall	C₄₁×C₉₇ ⋊ D₃
Hall	C₃×C₉₇ ⋊ D₄₁
Hall	C₃×C₄₁ ⋊ D₉₇
Sylow	C₉₇ ⋊ D₁₂₃
Sylow	C₄₁ ⋊ D₂₉₁
Sylow	C₃ ⋊ D₃₉₇₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₄₁×C₉₇	C₂
LCS	G ▷ C₃×C₄₁×C₉₇
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 141
transitive degree	μ_t(G) = 11931

A minimal faithful permutation representation — 2 generators on 141 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)(45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(2,3)(5,44)(6,43)(7,42)(8,41)(9,40)(10,39)(11,38)(12,37)(13,36)(14,35)(15,34)(16,33)(17,32)(18,31)(19,30)(20,29)(21,28)(22,27)(23,26)(24,25)(46,141)(47,140)(48,139)(49,138)(50,137)(51,136)(52,135)(53,134)(54,133)(55,132)(56,131)(57,130)(58,129)(59,128)(60,127)(61,126)(62,125)(63,124)(64,123)(65,122)(66,121)(67,120)(68,119)(69,118)(70,117)(71,116)(72,115)(73,114)(74,113)(75,112)(76,111)(77,110)(78,109)(79,108)(80,107)(81,106)(82,105)(83,104)(84,103)(85,102)(86,101)(87,100)(88,99)(89,98)(90,97)(91,96)(92,95)(93,94)

Polycyclic presentation:

2,3,41,97|b^a=b^2,c^a=c^40,d^a=d^96

Conjugacy classes & character table

5967 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23862, 9);

D11931 #37558790