D₁₆₇₉₁ #46777190

order	33582
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₆₇₉₁
unambiguous semidirect product	C₃⋊D₅₅₉₇
unambiguous semidirect product	C₂₉⋊D₅₇₉
unambiguous semidirect product	C₁₉₃⋊D₈₇

Splittings

Fitting, socle, derived, Hall	C₃×C₂₉×C₁₉₃ ⋊ C₂
Hall	C₂₉×C₁₉₃ ⋊ D₃
Hall	C₃×C₁₉₃ ⋊ D₂₉
Sylow	C₁₉₃ ⋊ D₈₇
Hall	C₃×C₂₉ ⋊ D₁₉₃
Sylow	C₂₉ ⋊ D₅₇₉
Sylow	C₃ ⋊ D₅₅₉₇

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₂₉×C₁₉₃	C₂
LCS	G ▷ C₃×C₂₉×C₁₉₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 225
transitive degree	μ_t(G) = 16791

A minimal faithful permutation representation — 2 generators on 225 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)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225);(2,3)(5,32)(6,31)(7,30)(8,29)(9,28)(10,27)(11,26)(12,25)(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(34,225)(35,224)(36,223)(37,222)(38,221)(39,220)(40,219)(41,218)(42,217)(43,216)(44,215)(45,214)(46,213)(47,212)(48,211)(49,210)(50,209)(51,208)(52,207)(53,206)(54,205)(55,204)(56,203)(57,202)(58,201)(59,200)(60,199)(61,198)(62,197)(63,196)(64,195)(65,194)(66,193)(67,192)(68,191)(69,190)(70,189)(71,188)(72,187)(73,186)(74,185)(75,184)(76,183)(77,182)(78,181)(79,180)(80,179)(81,178)(82,177)(83,176)(84,175)(85,174)(86,173)(87,172)(88,171)(89,170)(90,169)(91,168)(92,167)(93,166)(94,165)(95,164)(96,163)(97,162)(98,161)(99,160)(100,159)(101,158)(102,157)(103,156)(104,155)(105,154)(106,153)(107,152)(108,151)(109,150)(110,149)(111,148)(112,147)(113,146)(114,145)(115,144)(116,143)(117,142)(118,141)(119,140)(120,139)(121,138)(122,137)(123,136)(124,135)(125,134)(126,133)(127,132)(128,131)(129,130)

Polycyclic presentation:

2,3,29,193|b^a=b^2,c^a=c^28,d^a=d^192

Conjugacy classes & character table

8397 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33582, 9);

D16791 #46777190