Finite Group Databasebeta

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C₂×#72232155 #72325705

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

Aliases

Subgroups

At least 12192 conjugacy classes of subgroups; only the 37032 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

332 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((8,10)(12,16)(13,18)(21,26)(23,24), (7,8)(9,10)(11,12)(13,17)(14,18)(15,16)(19,20)(21,24)(22,25)(23,26), (11,13)(12,17)(14,16)(15,18), (4,6)(8,10)(13,18)(14,17)(19,21,22,26)(20,23,25,24), (1,2), (7,8)(9,10)(11,13)(12,17)(14,16)(15,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(11,14,15,17)(12,18,16,13)(19,20)(21,24)(22,25)(23,26));