Finite Group DatabasebetaFinite Group Databasebeta| order | 17876 |
| isoclinism | isoclinic class of D109 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×Dic109 |
| derived, Sylow | C109 ⋊ C4×C41 |
| Hall | C41×C109 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C41 | D109 |
| commutator, hypocenter | C109 | C4×C41 |
| Frattini | C2 | C41×D109 |
| Fitting, socle, prime radical | C2×C41×C109 | C2 |
| cosocle | C2×C109 | C2×C41 |
| LCS | G ▷ C109 | |
| UCS | C1 ◁ C2×C41 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17876 |
4592 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17876, 3);