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Aliases
Splittings
Subgroups
124 conjugacy classes of subgroups.
Full subgroup data →
Presentation
Polycyclic presentation:
2^3,5^3|a^2=c,d^a=d^2,e^a=e^3,f^a=f^3,d^b=d^4,e^b=e^4,d^c=d^4,e^c=e^4,f^c=f^4
Conjugacy classes & character table
34 conjugacy classes — view the full character table.
Relationships
| maximal subgroup of | AGL(1,𝔽5)×#1044, #14522936, #14522942, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1044, #14522936, #14522942, … |
| maximal quotient of | #14522692, #14522693, #14522694, … |
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1000, 170);
Finite Group Databasebeta