Finite Group Databasebeta

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C₂×#72232186 #72325783

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

Aliases

Subgroups

At least 20074 conjugacy classes of subgroups; only the 36856 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

368 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((4,6)(12,15)(13,17)(19,20,22,24)(21,25,26,23), (13,17)(16,18)(21,26)(23,25), (8,10)(12,15)(16,18)(21,26)(23,25), (1,2), (4,6)(13,17)(16,18)(21,26)(23,25), (3,4)(5,6)(7,8)(9,10)(11,12)(13,16)(14,15)(17,18)(19,20)(21,23)(22,24)(25,26), (3,4)(5,6)(11,13,14,17)(12,16,15,18)(19,21,22,26)(20,23,24,25));