Finite Group DatabasebetaFinite Group Databasebeta| order | 19568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C1223 ⋊ C2 |
| Sylow | C1223 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D1223 |
| commutator, cosocle | C4×C1223 | C22 |
| Frattini | C4 | C2×D1223 |
| Fitting | D4×C1223 | C2 |
| socle | C2×C1223 | D4 |
| hypercenter | D4 | D1223 |
| hypocenter | C1223 | D8 |
| LCS | G ▷ C4×C1223 ▷ C2×C1223 ▷ C1223 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9784 |
Polycyclic presentation:
2^4,1223|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^12223062 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19568, 25);