Finite Group Databasebeta

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C₂×#72232188 #72325682

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

Aliases

Subgroups

At least 23958 conjugacy classes of subgroups; only the 35600 normal subgroups are shown.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 26 points:

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

Conjugacy classes & character table

284 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)(12,13)(14,18)(19,20)(21,23)(22,25)(24,26), (4,6)(7,8)(9,10)(12,13)(14,18)(20,21)(24,25), (7,8)(9,10)(11,12,15,13)(14,16,18,17)(19,20,23,21)(22,24,26,25), (8,10)(22,26)(24,25), (1,2), (4,6)(7,8)(9,10)(11,13,15,12)(14,16,18,17)(19,21,23,20)(22,25,26,24), (3,4)(5,6)(7,8)(9,10)(11,14)(12,16)(13,17)(15,18)(19,22)(20,24)(21,25)(23,26));