Finite Group DatabasebetaFinite Group Databasebeta| order | 17710 |
| isoclinism | isoclinic class of D77 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C23 · Schur multiplier (H2) = C1 |
| direct product | C5×C23×D77 |
| unambiguous semidirect product | C7⋊(C5×D11×C23) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C23 | D77 |
| commutator, cosocle, hypocenter | C7×C11 | C2×C5×C23 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C11×C23 | C2 |
| LCS | G ▷ C7×C11 | |
| UCS | C1 ◁ C5×C23 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8855 |
4600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D23×D77, C5×D7×D11×C23, C5×D77⋊D23, … |
| maximal normal subgroup of | C5×D23×D77, C5×D7×D11×C23, C5×D77⋊D23, … |
| maximal quotient of | C5×C23×Dic77, C2×C5×C23×D77 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17710, 9);