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C₂²×#3099 #10575028

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

Aliases

Subgroups

8390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 28 points:

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

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 10482224);