Finite Group Databasebeta

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C₂×#72232133 #72325736

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

Aliases

Subgroups

At least 22546 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)(12,13)(14,18)(19,20)(21,24)(22,23)(25,26);(4,6)(14,18)(16,17)(20,23)(24,25);(11,12)(13,15)(14,17)(16,18);(7,8,9,10)(12,13)(16,17)(19,21)(20,24)(22,26)(23,25);(1,2);(4,6)(7,8)(9,10)(11,13,15,12)(14,17,18,16)(19,21)(20,24)(22,26)(23,25);(3,4)(5,6)(11,14)(12,16)(13,17)(15,18)(19,20)(21,25)(22,23)(24,26)

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