Finite Group DatabasebetaFinite Group Databasebeta| order | 19604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C169 · Schur multiplier (H2) = C1 |
| direct product | #1181×C169 |
| Fitting, Hall | C29×C169 ⋊ C4 |
| derived, Sylow | C29 ⋊ C4×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | #1181 |
| commutator, hypocenter | C29 | C4×C169 |
| Frattini | C13 | C13×#1181 |
| Fitting | C29×C169 | C4 |
| socle | C13×C29 | C4×C13 |
| prime radical, cosocle | C13×D29 | C2×C13 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C169 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4901 |
1859 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19604, 6);