Finite Group Databasebeta

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C₂×#72232150 #72325731

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

Aliases

Subgroups

At least 14072 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:

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

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