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C₂×#20265992 #27185897

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1408 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 135 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(107,118)(111,125)(115,129)(119,131)(123,134)(126,132)(128,135)(130,133);(104,107)(105,111)(106,115)(108,119)(109,118)(110,123)(112,126)(113,125)(114,128)(116,130)(117,129)(120,132)(121,133)(122,131)(124,134)(127,135);(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)(104,106,109,117)(105,110,113,124)(107,115,118,129)(108,121,122,116)(111,123,125,134)(112,127,120,114)(119,133,131,130)(126,135,132,128);(104,105,109,113)(106,114,117,127)(107,111,118,125)(108,120,122,112)(110,121,124,116)(115,128,129,135)(119,132,131,126)(123,133,134,130);(102,103)

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 19275);