Finite Group Databasebeta

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C₂×#20257285 #27124771

• 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)(58,61,62,70)(59,65,64,69)(60,68,67,73)(63,71,66,72);(60,67)(63,66)(68,73)(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)(50,53,54,52)(51,55,56,57)(59,64)(63,66)(65,69)(71,72);(50,52,54,53)(51,55,56,57)(58,60,62,67)(59,63,64,66)(61,68,70,73)(65,71,69,72);(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)(50,51)(52,55)(53,57)(54,56)(58,59)(60,66)(61,69)(62,64)(63,67)(65,70)(68,71)(72,73);(48,49)

Conjugacy classes & character table

1652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1078061);