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C₂×#45446 #7702091

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

Aliases

Subgroups

8692 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

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, 7609287);