Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C5 |
| direct product | C17×C7⋊#1044 |
| unambiguous semidirect product | C7⋊(C17×#1044) |
| Fitting, socle, Hall | C52×C7×C17 ⋊ C4 |
| derived, Hall | C52×C7 ⋊ C4×C17 |
| Hall | C52×C17 ⋊ Dic7 |
| Hall | C7×C17 ⋊ #1044 |
| Sylow | C52 ⋊ C17×Dic7 |
| Sylow | C7 ⋊ C17×#1044 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | C7⋊#1044 |
| commutator, hypocenter | C52×C7 | C4×C17 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7×C17 | C4 |
| prime radical | C7×C17×C5⋊D5 | C2 |
| cosocle | C7×C5⋊D5 | C2×C17 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C17 | |
64 conjugacy classes of subgroups.
884 conjugacy classes — view the full character table.
| maximal subgroup of | C17×C7⋊#64480, C17×ΓL(1,𝔽8)⋊#1044, C3×C17×C7⋊#1044, … |
| maximal normal subgroup of | C17×ΓL(1,𝔽8)⋊#1044, C3×C17×C7⋊#1044 |
| maximal quotient of | C3×C17×C7⋊#1044, C17×C3⋊(C7⋊#1044) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 79);