Finite Group Databasebeta

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C₂²×#1259666 #72334503

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

Aliases

Subgroups

At least 7986 conjugacy classes of subgroups; only the 42736 normal subgroups are shown.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

344 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)(15,19)(21,22)(23,26)(24,25)(27,28), (13,14)(15,18)(16,17)(19,20)(21,23)(22,26)(24,27)(25,28), (6,8)(10,12)(14,17)(18,20)(23,28)(26,27), (6,8)(13,14)(15,18)(16,17)(19,20)(21,23)(22,27)(24,26)(25,28), (5,6)(7,8)(9,10,11,12)(13,15,16,19)(14,18,17,20)(21,24,25,22)(23,27,28,26), (3,4), (1,2)(3,4));