Finite Group DatabasebetaFinite Group Databasebeta| order | 19604 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C29 · Schur multiplier (H2) = C1 |
| direct product | C29×#10621721 |
| Fitting, Hall | C29×C169 ⋊ C4 |
| derived, Sylow | C169 ⋊ C4×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | #10621721 |
| commutator, hypocenter | C169 | C4×C29 |
| Frattini | C13 | C29×#261 |
| Fitting | C29×C169 | C4 |
| socle | C13×C29 | #261 |
| prime radical | C29×D169 | C2 |
| cosocle | D169 | C2×C29 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C29 | |
18 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4901 |
1334 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19604, 7);