D₁₆₈₃₃ #46797574

order	33666
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₈₃₃
unambiguous semidirect product	C₃⋊D₅₆₁₁
unambiguous semidirect product	C₃₁⋊D₅₄₃
unambiguous semidirect product	C₁₈₁⋊D₉₃

Splittings

Fitting, socle, derived, Hall	C₃×C₃₁×C₁₈₁ ⋊ C₂
Hall	C₃₁×C₁₈₁ ⋊ D₃
Hall	C₃×C₁₈₁ ⋊ D₃₁
Sylow	C₁₈₁ ⋊ D₉₃
Hall	C₃×C₃₁ ⋊ D₁₈₁
Sylow	C₃₁ ⋊ D₅₄₃
Sylow	C₃ ⋊ D₅₆₁₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₃₁×C₁₈₁	C₂
LCS	G ▷ C₃×C₃₁×C₁₈₁
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 215
transitive degree	μ_t(G) = 16833

A minimal faithful permutation representation — 2 generators on 215 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)(35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215);(2,3)(5,34)(6,33)(7,32)(8,31)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)(36,215)(37,214)(38,213)(39,212)(40,211)(41,210)(42,209)(43,208)(44,207)(45,206)(46,205)(47,204)(48,203)(49,202)(50,201)(51,200)(52,199)(53,198)(54,197)(55,196)(56,195)(57,194)(58,193)(59,192)(60,191)(61,190)(62,189)(63,188)(64,187)(65,186)(66,185)(67,184)(68,183)(69,182)(70,181)(71,180)(72,179)(73,178)(74,177)(75,176)(76,175)(77,174)(78,173)(79,172)(80,171)(81,170)(82,169)(83,168)(84,167)(85,166)(86,165)(87,164)(88,163)(89,162)(90,161)(91,160)(92,159)(93,158)(94,157)(95,156)(96,155)(97,154)(98,153)(99,152)(100,151)(101,150)(102,149)(103,148)(104,147)(105,146)(106,145)(107,144)(108,143)(109,142)(110,141)(111,140)(112,139)(113,138)(114,137)(115,136)(116,135)(117,134)(118,133)(119,132)(120,131)(121,130)(122,129)(123,128)(124,127)(125,126)

Polycyclic presentation:

2,3,31,181|b^a=b^2,c^a=c^30,d^a=d^180

Conjugacy classes & character table

8418 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33666, 12);

D16833 #46797574