Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C31⋊#11744607 |
| derived, Hall | C31×C52⋊C9 ⋊ C4 |
| Hall | C52×C31 ⋊ Dic9 |
| Hall | C52⋊C9 ⋊ Dic31 |
| Sylow | C31 ⋊ #11744607 |
| Sylow | C52 ⋊ Dic279 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C31⋊#90646 |
| commutator, hypocenter | C31×C52⋊C9 | C4 |
| Frattini | C2×C3 | C31⋊#3874 |
| Fitting, socle, prime radical | C2×C3×C52×C31 | D3 |
| cosocle | C2×C31×C52⋊C9 | C2 |
| LCS | G ▷ C31×C52⋊C9 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,31,5^2,2,3|a^2=f,b^3=g^2,b^a=b^2g,c^a=c^30,d^a=d^2e,e^a=d^2e^3,g^a=g^2,d^b=d^2e^4,e^b=d^2e^21038 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 104);