Finite Group DatabasebetaFinite Group Databasebeta| order | 21776 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | C4×#19129602 |
| Fitting | C4×C1361 ⋊ C4 |
| derived, Sylow | C1361 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #19129602 |
| commutator, hypocenter | C1361 | C42 |
| Frattini | C2 | C2×#19129602 |
| Fitting | C4×C1361 | C4 |
| socle | C2×C1361 | C2×C4 |
| prime radical, cosocle | C2×D1361 | C22 |
| LCS | G ▷ C1361 | |
| UCS | C1 ◁ C4 | |
30 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5444 |
1376 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21776, 44);