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Dic7623 #44478789
Aliases
Splittings
Subgroups
54 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 141 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);(1,3,2,4)(6,13)(7,12)(8,11)(9,10)(15,20)(16,19)(17,18)(22,141)(23,140)(24,139)(25,138)(26,137)(27,136)(28,135)(29,134)(30,133)(31,132)(32,131)(33,130)(34,129)(35,128)(36,127)(37,126)(38,125)(39,124)(40,123)(41,122)(42,121)(43,120)(44,119)(45,118)(46,117)(47,116)(48,115)(49,114)(50,113)(51,112)(52,111)(53,110)(54,109)(55,108)(56,107)(57,106)(58,105)(59,104)(60,103)(61,102)(62,101)(63,100)(64,99)(65,98)(66,97)(67,96)(68,95)(69,94)(70,93)(71,92)(72,91)(73,90)(74,89)(75,88)(76,87)(77,86)(78,85)(79,84)(80,83)(81,82)
Polycyclic presentation:
2,3,7,11,2,3,11|a^2=e,b^3=f^2,d^11=g^10,b^a=b^2f,c^a=c^6,d^a=d^10g,f^a=f^2,g^a=g^10
Conjugacy classes & character table
7626 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(30492, 12);
Finite Group Databasebeta