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C₇⋊#564 #90377

• supersolvable
• metabelian
• solvable
• monomial
• stem

Aliases

Splittings

Subgroups

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 39 points:

(1,2,4,6,7,5,3)(9,15)(13,21)(14,23)(20,22)(24,27,28,35)(25,31,30,38)(26,33,32,34)(29,36,37,39);(8,11,12,19)(9,14,15,23)(10,16,17,18)(13,20,21,22)(25,30)(26,32)(31,38)(33,34);(8,10,12,17)(9,13,15,21)(11,18,19,16)(14,22,23,20)(24,26)(25,29)(27,34)(28,32)(30,37)(31,39)(33,35)(36,38);(2,3)(4,5)(6,7)(8,9)(10,13)(11,14)(12,15)(16,20)(17,21)(18,22)(19,23)(24,25,28,30)(26,29,32,37)(27,31,35,38)(33,36,34,39)

Polycyclic presentation:

2^6,7|a^2=f,b^2=e,c^2=e,d^2=f,c^a=cf,d^a=de,g^a=g^6,c^b=cef,d^b=df

Conjugacy classes & character table

61 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1139);