Finite Group DatabasebetaFinite Group Databasebeta| order | 8125 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C53×C13 · Schur multiplier (H2) = C54 |
| direct product | C5×C13×H(3,𝔽5) |
| unambiguous semidirect product | C52⋊(C52×C13) |
| unambiguous semidirect product | (C52×C13)⋊C52 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C52×C13 | C52 |
| commutator, Frattini | C5 | C53×C13 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C52×C13 ◁ G | |
260 conjugacy classes of subgroups.
1885 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8125, 12);