Finite Group Databasebeta

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C₂×#72232124 #72325762

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

Aliases

Subgroups

At least 22530 conjugacy classes of subgroups; only the 35624 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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