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C₂×#3212 #60781

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

Aliases

Subgroups

1109 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 53769);