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C₂³×#2572 #72301697

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

Aliases

Subgroups

94213 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 30 points:

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

Conjugacy classes & character table

304 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

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