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Dic4075 #30654381
Aliases
Splittings
Subgroups
18 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 192 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);(1,3,2,4)(6,29)(7,28)(8,27)(9,26)(10,25)(11,24)(12,23)(13,22)(14,21)(15,20)(16,19)(17,18)(31,192)(32,191)(33,190)(34,189)(35,188)(36,187)(37,186)(38,185)(39,184)(40,183)(41,182)(42,181)(43,180)(44,179)(45,178)(46,177)(47,176)(48,175)(49,174)(50,173)(51,172)(52,171)(53,170)(54,169)(55,168)(56,167)(57,166)(58,165)(59,164)(60,163)(61,162)(62,161)(63,160)(64,159)(65,158)(66,157)(67,156)(68,155)(69,154)(70,153)(71,152)(72,151)(73,150)(74,149)(75,148)(76,147)(77,146)(78,145)(79,144)(80,143)(81,142)(82,141)(83,140)(84,139)(85,138)(86,137)(87,136)(88,135)(89,134)(90,133)(91,132)(92,131)(93,130)(94,129)(95,128)(96,127)(97,126)(98,125)(99,124)(100,123)(101,122)(102,121)(103,120)(104,119)(105,118)(106,117)(107,116)(108,115)(109,114)(110,113)(111,112)
Polycyclic presentation:
2,5,163,2,5|a^2=d,b^5=e^4,b^a=b^4e,c^a=c^162,e^a=e^4
Conjugacy classes & character table
4078 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16300, 4);
Finite Group Databasebeta