Finite Group Databasebeta

?

← Prev (#28297985) Next (#28297987) →

C₂²×#16811460 #28297986

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

60366 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 73 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)(47,48)(49,50)(51,52)(58,61,62,69)(59,65,64,71)(60,68,67,73)(63,70,66,72);(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)(48,49)(50,51)(52,53)(59,64)(63,66)(65,71)(70,72);(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)(48,49)(50,51)(52,53)(60,67)(63,66)(68,73)(70,72);(58,60)(59,63)(61,68)(62,67)(64,66)(65,70)(69,73)(71,72);(58,59)(60,66)(61,65)(62,64)(63,67)(68,72)(69,71)(70,73);(56,57);(54,55)

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1083462);