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C₂×#45432 #7670070

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

Aliases

Subgroups

7742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7577266);