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C₂×#42532 #7640939

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

Aliases

Subgroups

7776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548135);