Finite Group DatabasebetaFinite Group Databasebeta| order | 17724 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C211 · Schur multiplier (H2) = C2 |
| direct product | C2×C3×D7×C211 |
| Fitting, socle | C2×C3×C7×C211 ⋊ C2 |
| derived, Sylow | C7 ⋊ C22×C3×C211 |
| Hall | C3×C7×C211 ⋊ C22 |
| Hall | C7×C211 ⋊ C22×C3 |
| Hall | C3×C7 ⋊ C22×C211 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C211 | D7 |
| commutator, cosocle, hypocenter | C7 | C22×C3×C211 |
| Frattini | C1 | G |
| Fitting, socle | C2×C3×C7×C211 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C2×C3×C211 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8862 |
6330 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17724, 78);