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C₂×#7910 #181002

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

Aliases

Subgroups

2074 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 88198);