Finite Group DatabasebetaFinite Group Databasebeta| order | 21780 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C5×C112 ⋊ C22 |
| Hall | C32×C112 ⋊ C2×D5 |
| Hall | C5×C112 ⋊ C2×C3⋊D3 |
| Sylow | C112 ⋊ D5×C3⋊D3 |
| Hall | C32×C5 ⋊ D112 |
| Sylow | C32 ⋊ D11×D55 |
| Sylow | C5 ⋊ #17983775 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C112 | C22 |
| LCS | G ▷ C32×C5×C112 | |
| UCS | C1 | |
360 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 61 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|e^a=e^4,f^a=f^10,g^a=g^10,c^b=c^2,d^b=d^2,g^b=g^101419 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21780, 716);