D₁₁₄₃₃ #37504186

order	22866
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₁₄₃₃
unambiguous semidirect product	C₃⋊D₃₈₁₁
unambiguous semidirect product	C₃₇⋊D₃₀₉
unambiguous semidirect product	C₁₀₃⋊D₁₁₁

Splittings

Fitting, socle, derived, Hall	C₃×C₃₇×C₁₀₃ ⋊ C₂
Hall	C₃₇×C₁₀₃ ⋊ D₃
Hall	C₃×C₁₀₃ ⋊ D₃₇
Hall	C₃×C₃₇ ⋊ D₁₀₃
Sylow	C₁₀₃ ⋊ D₁₁₁
Sylow	C₃₇ ⋊ D₃₀₉
Sylow	C₃ ⋊ D₃₈₁₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₇×C₁₀₃	C₂
LCS	G ▷ C₃×C₃₇×C₁₀₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 143
transitive degree	μ_t(G) = 11433

A minimal faithful permutation representation — 2 generators on 143 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)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143);(2,3)(5,40)(6,39)(7,38)(8,37)(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)(42,143)(43,142)(44,141)(45,140)(46,139)(47,138)(48,137)(49,136)(50,135)(51,134)(52,133)(53,132)(54,131)(55,130)(56,129)(57,128)(58,127)(59,126)(60,125)(61,124)(62,123)(63,122)(64,121)(65,120)(66,119)(67,118)(68,117)(69,116)(70,115)(71,114)(72,113)(73,112)(74,111)(75,110)(76,109)(77,108)(78,107)(79,106)(80,105)(81,104)(82,103)(83,102)(84,101)(85,100)(86,99)(87,98)(88,97)(89,96)(90,95)(91,94)(92,93)

Polycyclic presentation:

2,3,37,103|b^a=b^2,c^a=c^36,d^a=d^102

Conjugacy classes & character table

5718 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22866, 12);

D11433 #37504186