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C₂⁴×#400 #72325632

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

Aliases

Subgroups

146869 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

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

Conjugacy classes & character table

352 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)(21,22,25,23)(24,27,28,26), (10,12)(13,14)(15,18)(16,17)(19,20)(21,23,25,22)(24,27,28,26), (3,4), (5,6), (9,10)(11,12)(13,15,16,19)(14,18,17,20)(21,24)(22,26)(23,27)(25,28), (7,8), (1,2)(3,4)(5,6)(7,8));