Finite Group DatabasebetaFinite Group Databasebeta| order | 7900 |
| isoclinism | isoclinic class of D79 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×D79 |
| unambiguous semidirect product | C79⋊(C22×C52) |
| unambiguous semidirect product | (C2×C79)⋊(C2×C52) |
| Fitting, socle | C2×C52×C79 ⋊ C2 |
| derived, Sylow | C79 ⋊ C22×C52 |
| Hall | C52×C79 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C52 | D79 |
| commutator, hypocenter | C79 | C22×C52 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C79 | C2 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C52 | |
80 conjugacy classes of subgroups.
2050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D79⋊(C52⋊C3), C2×C52⋊C3×D79, C2×C52×D79⋊C3, … |
| maximal normal subgroup of | C2×D79⋊(C52⋊C3), C2×C52⋊C3×D79, C2×C52×D79⋊C3, … |
| maximal quotient of | C52×D3×D79, C2×C3×C52×D79, C2×C52×D237 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7900, 36);