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C₂×#46358 #7700314

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

Aliases

Subgroups

8448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7607510);