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C₂×#42427 #7641111

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

Aliases

Subgroups

8144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7548307);