Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×C7⋊#1039 |
| unambiguous semidirect product | C7⋊(C17×#1039) |
| derived, Hall | C52×C7 ⋊ C4×C17 |
| Hall | C52×C7×C17 ⋊ C4 |
| Hall | C52×C17 ⋊ Dic7 |
| Hall | C7×C17 ⋊ #1039 |
| Sylow | C52 ⋊ C17×Dic7 |
| Sylow | C7 ⋊ C17×#1039 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C17 | C5⋊D35 |
| commutator, hypocenter | C52×C7 | C4×C17 |
| Frattini | C2 | C17×C5⋊D35 |
| Fitting, socle, prime radical | C2×C52×C7×C17 | C2 |
| cosocle | C2×C52×C7 | C2×C17 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C2×C17 | |
96 conjugacy classes of subgroups.
3026 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 46);