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#153605

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial
• stem
• ambivalent

Aliases

No aliases for this group.

Subgroups

176 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 132 points:

(1,2)(3,4)(5,6,12,18)(7,19,24,64)(8,25,31,61)(9,32,36,93)(10,37,40,99)(11,41,39,17)(13,43,47,20)(14,48,52,28)(15,53,56,27)(16,57,59,34)(21,67,69,128)(22,70,71,130)(23,72,42,63)(26,54,79,121)(29,85,88,126)(30,89,87,75)(33,49,96,113)(35,97,81,92)(38,62,100,127)(44,104,106,77)(45,107,108,76)(46,66,60,102)(50,114,116,131)(51,84,101,111)(55,82,91,118)(58,103,123,65)(68,129,94,115)(73,110,124,80)(74,109,125,83)(78,122,90,120)(86,119,132,105)(95,117,98,112);(5,7,12,24)(6,13,18,47)(8,26,31,79)(9,33,36,96)(10,38,40,100)(11,42,39,23)(14,49,52,113)(15,54,56,121)(16,58,59,123)(17,60,41,46)(19,61,64,25)(20,48,43,28)(21,53,69,27)(22,57,71,34)(29,86,88,132)(30,90,87,78)(32,44,93,106)(35,98,81,95)(37,45,99,108)(50,115,116,129)(51,117,101,112)(55,122,91,120)(62,126,127,85)(63,75,72,89)(65,114,103,131)(66,84,102,111)(67,124,128,73)(68,82,94,118)(70,125,130,74)(76,110,107,80)(77,109,104,83)(92,119,97,105);(2,4)

Polycyclic presentation:

2^9|a^2=i,b^2=i,d^2=fg,f^2=gh,g^2=hi,h^2=i,b^a=bd,c^a=ce,d^a=df,f^a=fg,g^a=gh,h^a=hi,d^b=df,f^b=fg,g^b=gh,h^b=hi

Conjugacy classes & character table

89 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 60801);