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C₂²×#846389 #72334500

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

Aliases

Subgroups

2772752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 7 generators on 28 points:

(5,6)(7,8)(9,10)(11,12)(13,14)(15,19)(16,18)(17,20)(21,22)(23,27)(24,25)(26,28);(13,15)(14,17)(16,20)(18,19)(21,22)(23,26)(24,25)(27,28);(5,6,7,8)(10,12)(14,18)(15,20)(22,25)(26,27);(9,10)(11,12)(13,15)(14,17)(16,20)(18,19)(21,23)(22,26)(24,28)(25,27);(5,6)(7,8)(9,10)(11,12)(13,14)(15,17)(16,18)(19,20)(21,22)(23,26)(24,25)(27,28);(3,4);(1,2)(3,4)

Conjugacy classes & character table

368 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((5,6)(7,8)(9,10)(11,12)(13,14)(15,19)(16,18)(17,20)(21,22)(23,27)(24,25)(26,28), (13,15)(14,17)(16,20)(18,19)(21,22)(23,26)(24,25)(27,28), (5,6,7,8)(10,12)(14,18)(15,20)(22,25)(26,27), (9,10)(11,12)(13,15)(14,17)(16,20)(18,19)(21,23)(22,26)(24,28)(25,27), (5,6)(7,8)(9,10)(11,12)(13,14)(15,17)(16,18)(19,20)(21,22)(23,26)(24,25)(27,28), (3,4), (1,2)(3,4));