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C₂×#5625 #85961

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

1004 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 5 generators on 29 points:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(384, 18537);