Finite Group DatabasebetaFinite Group Databasebeta| order | 8875 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C52×C71 · Schur multiplier (H2) = C52 |
| direct product | C71×H(3,𝔽5) |
| unambiguous semidirect product | C52⋊(C5×C71) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C5×C71 | C52 |
| commutator, Frattini | C5 | C52×C71 |
| LCS | G ▷ C5 ▷ C1 | |
| UCS | C1 ◁ C5×C71 ◁ G | |
30 conjugacy classes of subgroups.
2059 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8875, 3);