Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C5 |
| direct product | #1039×C31⋊C9 |
| derived, Hall | C52×C31 ⋊ C4×C9 |
| Hall | C52×C31⋊C9 ⋊ C4 |
| Hall | C31×#1039 ⋊ C9 |
| Sylow | C31 ⋊ C9×#1039 |
| Sylow | C52 ⋊ C4×C31⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C5⋊D5×C31⋊C3 |
| commutator, hypocenter | C52×C31 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C52×C31 | C2×C3 |
| LCS | G ▷ C52×C31 | |
| UCS | C1 ◁ C2×C3 | |
144 conjugacy classes of subgroups.
1092 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 102);