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C₂×#33606 #7622965

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

Aliases

Subgroups

2032 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 38 points:

(1,2);(3,4)(5,6)(7,8,12,16)(9,17,19,31)(10,22,24,37)(11,25,23,15)(13,26,27,20)(14,29,30,18)(21,36,35,33)(28,34,32,38);(7,9,18,34,11,21,24,26,12,19,29,38,23,35,10,20)(8,13,22,33,15,28,30,31,16,27,37,36,25,32,14,17);(4,6);(9,19)(13,27)(17,31)(20,26)(21,35)(28,32)(33,36)(34,38)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7530161);