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C₂×#9494 #201607

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

Aliases

Subgroups

1420 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4,7,10,8,11,6,16)(5,12,15,17,13,18,14,9)(19,20)(21,27)(22,25,32,34)(23,29)(24,26)(28,33,30,31);(3,5,8,13)(4,9)(6,14,7,15)(10,12)(11,17)(16,18)(19,21,27,20,24,29,23,26)(22,30,31,34,32,28,33,25);(5,13)(9,17)(12,18)(14,15)(19,22)(20,25)(21,28)(23,33)(24,32)(26,34)(27,31)(29,30)

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 108803);