Finite Group DatabasebetaFinite Group Databasebeta| order | 17756 |
| isoclinism | isoclinic class of D23 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C193 · Schur multiplier (H2) = C1 |
| direct product | Dic23×C193 |
| unambiguous semidirect product | C23⋊(C4×C193) |
| derived, Sylow | C23 ⋊ C4×C193 |
| Hall | C23×C193 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C193 | D23 |
| commutator, hypocenter | C23 | C4×C193 |
| Frattini | C2 | D23×C193 |
| Fitting, socle, prime radical | C2×C23×C193 | C2 |
| cosocle | C2×C23 | C2×C193 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C2×C193 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17756 |
5018 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17756, 2);