Finite Group DatabasebetaFinite Group Databasebeta| order | 17892 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3 |
| derived, Sylow | C71 ⋊ C32×C4×C7 |
| Hall | C32×C71⋊C7 ⋊ C4 |
| Hall | C32×Dic71 ⋊ C7 |
| Hall | C32×C71 ⋊ C4×C7 |
| Hall | C71⋊C7 ⋊ C32×C4 |
| Hall | Dic71 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D71⋊C7 |
| commutator, hypocenter | C71 | C32×C4×C7 |
| Frattini | C2 | C32×D71⋊C7 |
| Fitting, socle | C2×C32×C71 | C2×C7 |
| prime radical | C2×C32×C71⋊C7 | C2 |
| cosocle | C2×C71 | C2×C32×C7 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2556 |
342 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17892, 46);