Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C5⋊D5)⋊D119 |
| 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 ⋊ (C5⋊D5)⋊D7 |
| Sylow | C7 ⋊ (C5⋊D5)⋊D17 |
| 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.
Polycyclic presentation:
2^2,5^2,7,17|c^a=c^4,e^a=e^6,f^a=f^16,c^b=c^4,d^b=d^4842 conjugacy classes — view the full character table.
| maximal subgroup of | ((C5⋊D5)⋊C3)⋊D119, ((C5⋊D5)⋊D119)⋊C3, C3×(C5⋊D5)⋊D119, … |
| maximal normal subgroup of | ((C5⋊D5)⋊D119)⋊C3, C3×(C5⋊D5)⋊D119 |
| maximal quotient of | C3×(C5⋊D5)⋊D119, #49087984, #49087989 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 107);