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C₂×#48812 #7704212

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

Aliases

Subgroups

8034 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

(1,2);(4,6)(7,8,11,12)(9,13,14,10)(15,16)(17,24)(18,22)(19,27)(20,21)(23,28)(25,26)(29,30);(8,12)(10,13)(16,21)(17,22)(19,28)(26,30);(3,4,5,6)(7,9)(8,10)(11,14)(12,13)(15,17)(16,18)(19,25)(20,22)(21,24)(23,26)(27,30)(28,29);(7,10)(8,9)(11,13)(12,14)(15,18)(16,22)(17,21)(19,26)(20,24)(23,29)(25,27)(28,30);(7,9)(8,10)(11,14)(12,13)(15,19)(16,23)(17,25)(18,26)(20,28)(21,27)(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, 7611408);