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C₂×#50890 #7706673

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

Aliases

Subgroups

7658 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7613869);