Finite Group Databasebeta

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C₂×#72221845 #72244116

• supersolvable
• metabelian
• solvable
• monomial

Aliases

Splittings

Subgroups

4305 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 3 generators on 56 points:

(3,9,10)(6,15,16)(8,18,19)(12,21,22)(14,24,25)(20,26,27)(29,32)(30,36)(31,40)(33,41)(34,45)(35,43)(37,38)(39,49)(42,48)(44,52)(46,51)(47,54)(50,53);(1,3,8)(2,6,14)(4,10,18)(5,12,20)(7,16,24)(9,19,11)(13,22,26)(15,25,17)(21,27,23)(28,39,36,31,37,38,40,30,49)(29,34,46,35,47,53,33,44,48)(32,51,54,41,42,45,43,50,52)(55,56);(1,7,23,4,17,5,11,2,13)(3,16,21,10,15,12,9,6,22)(8,24,27,18,25,20,19,14,26)(28,29,32)(30,44,50)(31,35,41)(33,43,40)(34,51,39)(36,46,54)(37,47,42)(38,53,45)(48,52,49)

Conjugacy classes & character table

414 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((3,9,10)(6,15,16)(8,18,19)(12,21,22)(14,24,25)(20,26,27)(29,32)(30,36)(31,40)(33,41)(34,45)(35,43)(37,38)(39,49)(42,48)(44,52)(46,51)(47,54)(50,53), (1,3,8)(2,6,14)(4,10,18)(5,12,20)(7,16,24)(9,19,11)(13,22,26)(15,25,17)(21,27,23)(28,39,36,31,37,38,40,30,49)(29,34,46,35,47,53,33,44,48)(32,51,54,41,42,45,43,50,52)(55,56), (1,7,23,4,17,5,11,2,13)(3,16,21,10,15,12,9,6,22)(8,24,27,18,25,20,19,14,26)(28,29,32)(30,44,50)(31,35,41)(33,43,40)(34,51,39)(36,46,54)(37,47,42)(38,53,45)(48,52,49));