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C₂×#23557 #6431981

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

Aliases

Subgroups

3606 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 30 points:

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

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, 6339177);