Finite Group Databasebeta

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C₂×#72232118 #72325725

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

Aliases

Subgroups

At least 21986 conjugacy classes of subgroups; only the 36208 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

308 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)(11,12)(13,15)(14,17)(16,18)(19,20)(21,25)(22,23)(24,26), (4,6)(7,8)(9,10)(11,12)(13,15)(14,16)(17,18)(19,21)(20,24)(22,25)(23,26), (12,13)(14,18)(20,22)(21,26), (8,10)(12,13)(16,17)(20,22)(21,26), (1,2), (4,6)(7,8)(9,10)(11,13,15,12)(14,16,18,17)(19,22,23,20)(21,24,26,25), (3,4)(5,6)(11,14)(12,16)(13,17)(15,18)(19,21)(20,24)(22,25)(23,26));