Finite Group DatabasebetaFinite Group Databasebeta| order | 17700 |
| isoclinism | isoclinic class of #1044 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C59 · Schur multiplier (H2) = C5 |
| direct product | C3×C59×#1044 |
| Fitting, socle, Hall | C3×C52×C59 ⋊ C4 |
| derived, Sylow | C52 ⋊ C3×C4×C59 |
| Hall | C52×C59 ⋊ C3×C4 |
| Hall | C3×C52 ⋊ C4×C59 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C59 | #1044 |
| commutator, hypocenter | C52 | C3×C4×C59 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C59 | C4 |
| prime radical | C3×C5⋊D5×C59 | C2 |
| cosocle | C5⋊D5 | C2×C3×C59 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C3×C59 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1770 |
1770 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17700, 67);