Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊D3)⋊#11925890 |
| Fitting, socle, Hall | C32×C112 ⋊ C2×D5 |
| derived, Hall | C32×#10597245 ⋊ C22 |
| Hall | #10597245 ⋊ D32 |
| Sylow | C112 ⋊ (C3⋊D3)⋊D5 |
| Sylow | C32 ⋊ C2×#11925890 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C32×#10597245 | C22 |
| Fitting, socle | C32×C112 | C2×D5 |
| LCS | G ▷ C32×#10597245 | |
| UCS | C1 | |
156 conjugacy classes of subgroups; only the 20 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 20 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^2,3^2,5,11^2|d^a=d^2,e^a=e^4,f^a=f^3g^3,g^a=fg^8,c^b=c^2,d^b=d^2,f^e=f^4g^8,g^e=g^3153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 461);