Finite Group DatabasebetaFinite Group Databasebeta| order | 17710 |
| isoclinism | isoclinic class of D55 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7×C23 · Schur multiplier (H2) = C1 |
| direct product | C7×C23×D55 |
| unambiguous semidirect product | C5⋊(C7×D11×C23) |
| unambiguous semidirect product | C11⋊(C7×D5×C23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C23 | D55 |
| commutator, cosocle, hypocenter | C5×C11 | C2×C7×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11×C23 | C2 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C7×C23 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8855 |
4669 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C7×D23×D55, C7×D5×D11×C23, C7×D55⋊D23, … |
| maximal normal subgroup of | C7×D23×D55, C7×D5×D11×C23, C7×D55⋊D23, … |
| maximal quotient of | C7×C23×Dic55, C2×C7×C23×D55 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17710, 13);