Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C2 |
| direct product | C2×C5×D595 |
| unambiguous semidirect product | (C2×C5)⋊(C5×D119) |
| unambiguous semidirect product | (C2×C7)⋊(C5×D85) |
| unambiguous semidirect product | (C2×C17)⋊(C5×D35) |
| Fitting, socle | C2×C52×C7×C17 ⋊ C2 |
| derived | C5×C7×C17 ⋊ C22×C5 |
| Hall | C52×C7×C17 ⋊ C22 |
| Hall | C52×C17 ⋊ C2×D7 |
| Hall | C52×C7 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×C5×D5 |
| Sylow | C52 ⋊ C2×D119 |
| Sylow | C17 ⋊ C2×C5×D35 |
| Sylow | C7 ⋊ C2×C5×D85 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D595 |
| commutator, cosocle, hypocenter | C5×C7×C17 | C22×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7×C17 | C2 |
| LCS | G ▷ C5×C7×C17 | |
| UCS | C1 ◁ C2×C5 | |
96 conjugacy classes of subgroups.
2990 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7⋊(C17⋊#3874), C2×C5×C5⋊(C17⋊AGL(1,𝔽7)), C5×D3×D595, … |
| maximal normal subgroup of | C2×C5×C5⋊(C17⋊AGL(1,𝔽7)), C2×C3×C5×D595 |
| maximal quotient of | C5×D3×D595, C2×C3×C5×D595, C2×C5×D1785 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 112);