Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D5×D595 |
| unambiguous semidirect product | (C5×D5)⋊D119 |
| unambiguous semidirect product | (C7×D5)⋊D85 |
| unambiguous semidirect product | (D5×C17)⋊D35 |
| Fitting, socle, derived, Hall | C52×C7×C17 ⋊ C22 |
| Hall | C52×C17 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ D52 |
| Sylow | C52 ⋊ C2×D119 |
| Sylow | C17 ⋊ D5×D35 |
| Sylow | C7 ⋊ D5×D85 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7×C17 | C22 |
| LCS | G ▷ C52×C7×C17 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
1196 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3874⋊D119, D5×C5⋊(C17⋊AGL(1,𝔽7)), C3×D5×D595, … |
| maximal normal subgroup of | D5×C5⋊(C17⋊AGL(1,𝔽7)), C3×D5×D595 |
| maximal quotient of | C3×D5×D595, D5×D1785, D15×D595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 102);