Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C3 |
| direct product | C5×C31⋊#4380 |
| Fitting, socle, Hall | C32×C52×C31 ⋊ C4 |
| derived | C32×C5×C31 ⋊ C4×C5 |
| Hall | C52×C31 ⋊ #157 |
| Hall | C32×C31 ⋊ C5×AGL(1,𝔽5) |
| Hall | C32×C52 ⋊ Dic31 |
| Sylow | C31 ⋊ C5×#4380 |
| Sylow | C52 ⋊ C31⋊#157 |
| Sylow | C32 ⋊ C5×C31⋊AGL(1,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C31⋊#4380 |
| commutator, hypocenter | C32×C5×C31 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C31 | C4 |
| prime radical | C5×C31×C3⋊D15 | C2 |
| cosocle | C31×C3⋊D15 | C2×C5 |
| LCS | G ▷ C32×C5×C31 | |
| UCS | C1 ◁ C5 | |
92 conjugacy classes of subgroups.
1875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 622);