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C₂×#41953 #7640396

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

Aliases

Subgroups

7918 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 30 points:

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

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, 7547592);