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C₂×#63024 #10586344

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

Aliases

Subgroups

35128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10493540);