Finite Group DatabasebetaFinite Group Databasebeta| order | 7900 |
| isoclinism | isoclinic class of D25 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C79 · Schur multiplier (H2) = C1 |
| direct product | C79×Dic25 |
| derived, Sylow | C25 ⋊ C4×C79 |
| Hall | C25×C79 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C79 | D25 |
| commutator, hypocenter | C25 | C4×C79 |
| Frattini | C2×C5 | D5×C79 |
| Fitting | C2×C25×C79 | C2 |
| socle | C2×C5×C79 | D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C2×C79 | |
18 conjugacy classes of subgroups.
2212 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C79×Dic25, C79×Dic75, Dic25×C79⋊C3 |
| maximal normal subgroup of | C3×C79×Dic25, Dic25×C79⋊C3 |
| maximal quotient of | C3×C79×Dic25, C79×Dic75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7900, 2);