Finite Group Databasebeta

?

← Prev (#27123448) Next (#27123450) →

C₂×#20257677 #27123449

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

7258 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)(58,62,63,61)(59,65,66,71)(60,68,69,70)(64,73,67,72);(51,55)(54,57)(58,61,63,62)(59,65,66,71)(60,68,69,70)(64,72,67,73);(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);(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)(50,52)(51,54)(53,56)(55,57)(58,60)(59,64)(61,70)(62,68)(63,69)(65,73)(66,67)(71,72);(50,51)(52,54)(53,55)(56,57)(58,59)(60,67)(61,65)(62,71)(63,66)(64,69)(68,73)(70,72);(48,49)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12032, 1076739);