Finite Group DatabasebetaFinite Group Databasebeta| order | 16770 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5×C43 · Schur multiplier (H2) = C1 |
| direct product | C3×C5×D13×C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C5×C43 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C3×C5×C43 |
| Frattini | C1 | G |
| Fitting, socle | C3×C5×C13×C43 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C3×C5×C43 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8385 |
5160 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C5×C43×#261, C3×C5×C43⋊#261, C3×C5×D13×D43, … |
| maximal normal subgroup of | C3×C5×C43×#261, C3×C5×C43⋊#261, C3×C5×D13×D43, … |
| maximal quotient of | C3×C5×C43×Dic13, C2×C3×C5×D13×C43 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16770, 7);