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C₂×#42468 #7641101

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

6642 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4,7,8)(5,6,10,9)(19,20)(21,25)(22,24)(23,26);(4,8)(6,9)(11,12)(13,17)(14,15)(16,18)(19,20,22,24)(21,23,26,25);(4,8)(5,10)(12,15)(16,17)(19,20)(21,23)(22,24)(25,26);(3,5,7,10)(4,9,8,6)(11,12)(13,16)(14,15)(17,18)(19,21,22,26)(20,23,24,25);(3,6,7,9)(4,10,8,5)(11,13,14,18)(12,16,15,17)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7548297);