Finite Group DatabasebetaFinite Group Databasebeta| order | 8875 |
| isoclinism | isoclinic class of C71⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C53 |
| direct product | C52×C71⋊C5 |
| unambiguous semidirect product | C71⋊C53 |
| unambiguous semidirect product | (C5×C71)⋊C52 |
| Fitting, socle | C52×C71 ⋊ C5 |
| derived, Sylow | C71 ⋊ C53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | C71⋊C5 |
| commutator, hypocenter | C71 | C53 |
| Frattini | C1 | G |
| Fitting, socle | C52×C71 | C5 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C52 | |
128 conjugacy classes of subgroups.
475 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8875, 15);