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C₂³×#3485 #72324516

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

Aliases

Subgroups

848581 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 26 points:

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

Conjugacy classes & character table

352 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((7,8)(9,10)(11,12,15,18)(13,19,20,16)(14,17,23,22)(21,25,26,24), (7,8)(9,10)(13,20)(16,19)(21,26)(24,25), (3,4), (5,6), (11,13)(12,16)(14,21)(15,20)(17,24)(18,19)(22,25)(23,26), (1,2)(3,4)(5,6), (8,10)(11,14)(12,17)(13,21)(15,23)(16,24)(18,22)(19,25)(20,26), (7,8)(9,10)(11,12)(13,19)(14,22)(15,18)(16,20)(17,23)(21,24)(25,26));