Finite Group DatabasebetaFinite Group Databasebeta| order | 19472 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C2×#23753593 |
| derived, Sylow | C1217 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #19096454 |
| commutator, hypocenter | C1217 | C2×C8 |
| Frattini | C2 | C2×#19096454 |
| Fitting, socle, prime radical | C22×C1217 | C4 |
| cosocle | Dic1217 | C22 |
| LCS | G ▷ C1217 | |
| UCS | C1 ◁ C22 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19472 |
1232 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19472, 47);