Finite Group Databasebeta

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C₂×#72232087 #72325677

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

Aliases

Subgroups

At least 22502 conjugacy classes of subgroups; only the 35496 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

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