Finite Group DatabasebetaFinite Group Databasebeta| order | 8300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C5 |
| direct product | C5⋊D5×D83 |
| unambiguous semidirect product | (C5×D83)⋊D5 |
| Fitting, socle, derived, Hall | C52×C83 ⋊ C22 |
| Sylow | C83 ⋊ C2×C5⋊D5 |
| Sylow | C52 ⋊ C2×D83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C83 | C22 |
| LCS | G ▷ C52×C83 | |
| UCS | C1 | |
80 conjugacy classes of subgroups.
602 conjugacy classes — view the full character table.
| maximal subgroup of | (C5⋊D5)⋊C3×D83, C3×C5⋊D5×D83, C3⋊(C5⋊D5)×D83, … |
| maximal normal subgroup of | (C5⋊D5)⋊C3×D83, C3×C5⋊D5×D83 |
| maximal quotient of | C3×C5⋊D5×D83, C3⋊(C5⋊D5)×D83, C5⋊D5×D249, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8300, 28);