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C₂×#33674 #7623075

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

Aliases

Subgroups

1776 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)(13,18)(14,17)(15,24)(16,20)(19,22)(21,25)(23,26);(4,7)(8,10);(12,17)(13,15)(14,22)(18,19)(20,26)(21,23)(24,25);(3,5,6,9)(4,8,7,10)(11,13,16,15)(12,18,20,24)(14,21,23,22)(17,25,26,19)

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530271);