Finite Group Databasebeta

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C₂×#20257600 #27123484

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

7302 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 73 points:

(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(59,65)(63,66)(64,73)(71,72);(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)(51,55)(54,57)(58,61,62,70)(59,64,65,73)(60,67,68,69)(63,71,66,72);(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)(51,55)(52,56);(50,52)(51,54)(53,56)(55,57)(58,60,62,68)(59,63,65,66)(61,69,70,67)(64,72,73,71);(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)(50,51)(52,54)(53,55)(56,57)(58,59)(60,66)(61,64)(62,65)(63,68)(67,72)(69,71)(70,73);(48,49)

Conjugacy classes & character table

1226 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076774);