Finite Group DatabasebetaFinite Group Databasebeta| order | 27900 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C52×C31 ⋊ C22 |
| Hall | C52×C31 ⋊ D32 |
| Hall | C32×C31 ⋊ D52 |
| Hall | C32×C52 ⋊ C2×D31 |
| Sylow | C31 ⋊ D15⋊D15 |
| Sylow | C52 ⋊ (C3⋊D3)⋊D31 |
| Sylow | C32 ⋊ D5×D155 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C52×C31 | C22 |
| LCS | G ▷ C32×C52×C31 | |
| UCS | C1 | |
212 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^2,3^2,5^2,31|d^a=d^2,f^a=f^4,g^a=g^30,c^b=c^2,d^b=d^2,e^b=e^41875 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27900, 685);