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C₂×#7898 #180964

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

Aliases

Subgroups

2050 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 30 points:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88160);