Finite Group Databasebeta

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C₂²×#15689875 #27123164

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

7238 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 75 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)(53,57)(56,59)(61,67)(62,70)(66,75)(69,71);(53,57)(54,58)(60,63,64,72)(61,66,67,75)(62,69,70,71)(65,73,68,74);(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)(52,54)(53,56)(55,58)(57,59)(60,62,64,70)(61,65,67,68)(63,71,72,69)(66,74,75,73);(52,53)(54,56)(55,57)(58,59)(60,61,64,67)(62,68,70,65)(63,66,72,75)(69,74,71,73);(50,51);(48,49)

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076454);