Finite Group Databasebeta

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C₂×#72232093 #72325666

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

Aliases

Subgroups

At least 24008 conjugacy classes of subgroups; only the 35424 normal subgroups are shown.

Full subgroup data →

Presentation

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

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