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C₂×#72323418 #72332968

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

Aliases

Subgroups

At least 12856 conjugacy classes of subgroups; only the 35256 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

272 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)(11,12)(13,15)(14,16)(17,18), (7,8)(9,10)(11,13)(12,15)(14,17)(16,18)(19,20)(21,24)(22,25)(23,26), (11,12,14,16)(13,15,17,18)(19,21,23,25)(20,24,26,22), (1,2), (4,6)(12,16)(13,17)(19,21,23,25)(20,22,26,24), (11,12)(13,15)(14,16)(17,18)(19,21)(20,24)(22,26)(23,25), (3,4)(5,6)(11,13)(12,15)(14,17)(16,18)(19,22,23,24)(20,25,26,21));