Finite Group DatabasebetaFinite Group Databasebeta| order | 8300 |
| isoclinism | isoclinic class of C5⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C83 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C5⋊D5×C83 |
| unambiguous semidirect product | (C2×C5)⋊(D5×C83) |
| Fitting, socle | C2×C52×C83 ⋊ C2 |
| derived, Sylow | C52 ⋊ C22×C83 |
| Hall | C52×C83 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C83 | C5⋊D5 |
| commutator, hypocenter | C52 | C22×C83 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C83 | C2 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C83 | |
80 conjugacy classes of subgroups.
2324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C83×(C5⋊D5)⋊C3, D3×C5⋊D5×C83, C2×C3×C5⋊D5×C83, … |
| maximal normal subgroup of | C2×C83×(C5⋊D5)⋊C3, C2×C3×C5⋊D5×C83 |
| maximal quotient of | D3×C5⋊D5×C83, C2×C3×C5⋊D5×C83, C2×C83×C3⋊(C5⋊D5) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8300, 33);