Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| isoclinism | isoclinic class of D31 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5 |
| direct product | C32×C52×Dic31 |
| derived, Sylow | C31 ⋊ C32×C4×C52 |
| Hall | C32×C52×C31 ⋊ C4 |
| Hall | C52×C31 ⋊ C32×C4 |
| Hall | C32×C31 ⋊ C4×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32×C52 | D31 |
| commutator, hypocenter | C31 | C32×C4×C52 |
| Frattini | C2 | C32×C52×D31 |
| Fitting, socle, prime radical | C2×C32×C52×C31 | C2 |
| cosocle | C2×C31 | C2×C32×C52 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C2×C32×C52 | |
288 conjugacy classes of subgroups.
7650 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 415);