Finite Group Databasebeta

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#28310331

• supersolvable
• metabelian
• solvable
• monomial

Aliases

No aliases for this group.

Splittings

Subgroups

570 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^8,53|a^2=e,b^2=f,d^2=gh,e^2=h,f^2=gh,g^2=h,b^a=bd,d^a=dg,f^a=fg,g^a=gh,i^a=i^23,d^b=dh,i^b=i^30,i^c=i^52,i^e=i^52,i^f=i^52

Conjugacy classes & character table

428 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1095807);