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C₂²×#2032000 #72296947

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

Aliases

Subgroups

At least 8088 conjugacy classes of subgroups; only the 38920 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

320 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((10,12)(14,17)(18,20)(23,27)(26,28), (9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,22)(23,26)(24,25)(27,28), (6,8)(9,10,11,12)(14,17)(15,19)(22,25)(26,28), (5,6)(7,8)(9,10)(11,12)(13,14)(15,18)(16,17)(19,20)(21,23)(22,26)(24,27)(25,28), (5,6)(7,8)(9,10)(11,12)(13,15)(14,18)(16,19)(17,20)(21,22)(23,26)(24,25)(27,28), (3,4), (1,2)(3,4));