Finite Group Databasebeta

?

← Prev (#27142855) Next (#27142857) →

#27142856

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

No aliases for this group.

Splittings

Subgroups

342 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 133 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)(102,105,108,123)(103,110,113,129)(104,115,118,132)(106,122,107,121)(109,124,126,130)(111,128,112,119)(114,127,125,133)(116,120,117,131);(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)(99,101)(102,104)(103,109)(105,120)(106,117)(107,116)(108,118)(110,127)(111,125)(112,114)(113,126)(115,122)(119,130)(121,132)(123,131)(124,128)(129,133);(98,99)(100,101)(102,103,108,113)(104,114,118,125)(105,119,123,128)(106,112,107,111)(109,117,126,116)(110,122,129,121)(115,130,132,124)(120,127,131,133)

Polycyclic presentation:

2^7,97|a^2=g,c^2=g,d^2=g,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cf,d^b=dg,f^b=fg,h^b=h^96,d^c=dg,e^c=eg,f^c=fg,h^c=h^96

Conjugacy classes & character table

1082 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12416, 5630);