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C₂×#3153 #60638

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

Aliases

Subgroups

1695 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 22 points:

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

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, 53626);