Finite Group DatabasebetaFinite Group Databasebeta| order | 11900 |
| isoclinism | isoclinic class of D119 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×Dic119 |
| unambiguous semidirect product | C7⋊(C25×Dic17) |
| derived, Hall | C7×C17 ⋊ C4×C25 |
| Hall | C7×C17×C25 ⋊ C4 |
| Hall | C17×C25 ⋊ Dic7 |
| Hall | C7×C25 ⋊ Dic17 |
| Sylow | C17 ⋊ C25×Dic7 |
| Sylow | C7 ⋊ C25×Dic17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C25 | D119 |
| commutator, hypocenter | C7×C17 | C4×C25 |
| Frattini | C2×C5 | C5×D119 |
| Fitting | C2×C7×C17×C25 | C2 |
| socle, prime radical, cosocle | C2×C5×C7×C17 | C2×C5 |
| LCS | G ▷ C7×C17 | |
| UCS | C1 ◁ C2×C25 | |
36 conjugacy classes of subgroups.
3050 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C25×Dic119, C25×Dic357, C25×ΓL(1,𝔽8)⋊Dic17 |
| maximal normal subgroup of | C3×C25×Dic119, C25×ΓL(1,𝔽8)⋊Dic17 |
| maximal quotient of | C3×C25×Dic119, C25×Dic357 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11900, 4);