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C₂×#8018 #181512

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

Aliases

Subgroups

1946 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 88708);