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C₂²×#62876 #72301262

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

Aliases

Subgroups

481669 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 28 points:

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

Conjugacy classes & character table

280 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((5,6,9,12)(7,10,11,8)(13,14)(15,20)(16,21)(17,22)(18,19)(23,28)(24,25)(26,27), (5,6)(7,10)(8,11)(9,12)(14,19)(17,20)(21,27)(25,28), (5,7,9,11)(6,10,12,8)(15,22)(17,20)(23,24)(25,28), (5,6)(7,8)(9,12)(10,11)(13,15)(14,20)(16,24)(17,19)(18,22)(21,25)(23,26)(27,28), (5,8)(6,11)(7,12)(9,10)(13,16)(14,21)(15,23)(17,25)(18,26)(19,27)(20,28)(22,24), (13,17,18,20)(14,22,19,15)(16,25,26,28)(21,24,27,23), (3,4), (1,2)(3,4));