Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | #1042×#4294 |
| derived, Hall | C52×C19 ⋊ C4×C9 |
| Hall | C52×#4294 ⋊ C4 |
| Hall | C19×#1042 ⋊ C9 |
| Sylow | C52 ⋊ C4×#4294 |
| Sylow | C19 ⋊ C9×#1042 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C19⋊C3×#1042 |
| commutator, hypocenter | C52×C19 | C4×C9 |
| Fitting, socle | C3×C52×C19 | C3×C4 |
| prime radical, cosocle | C3×C5×D5×C19 | C2×C3 |
| LCS | G ▷ C52×C19 | |
| UCS | C1 ◁ C3 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3420 |
351 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 179);