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C₂×#3096 #60512

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

Aliases

Subgroups

1181 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 26 points:

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

Conjugacy classes & character table

64 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(256, 53500);