Finite Group DatabasebetaFinite Group Databasebeta| order | 21536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#14582089 |
| Fitting | Q8×C673 ⋊ C4 |
| Sylow | C673 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#14582089 |
| commutator, socle | C2×C673 | C22×C4 |
| Fitting | Q8×C673 | C4 |
| prime radical, cosocle | C2×D673 | C23 |
| hypercenter | Q8 | #14582089 |
| hypocenter | C673 | C4×Q8 |
| LCS | G ▷ C2×C673 ▷ C673 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5384 |
860 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21536, 227);