Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| isoclinism | isoclinic class of #1042 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C19 · Schur multiplier (H2) = C3 |
| direct product | C32×C19×#1042 |
| Fitting, socle, Hall | C32×C52×C19 ⋊ C4 |
| derived, Sylow | C52 ⋊ C32×C4×C19 |
| Hall | C52×C19 ⋊ C32×C4 |
| Hall | C32×C52 ⋊ C4×C19 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C19 | #1042 |
| commutator, hypocenter | C52 | C32×C4×C19 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C19 | C4 |
| prime radical | C32×C5×D5×C19 | C2 |
| cosocle | C5×D5 | C2×C32×C19 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C32×C19 | |
156 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3420 |
2223 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 499);