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C₂×#33951 #7623917

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

Aliases

Subgroups

1400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

86 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7531113);