Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| isoclinism | isoclinic class of D7 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C5×C17 · Schur multiplier (H2) = C3 |
| direct product | C32×C5×D7×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32×C5×C17 | D7 |
| commutator, cosocle, hypocenter | C7 | C2×C32×C5×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C17 | C2 |
| LCS | G ▷ C7 | |
| UCS | C1 ◁ C32×C5×C17 | |
96 conjugacy classes of subgroups.
3825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×C5×D7×D17, C32×D5×D7×C17, C32×D7×D85, … |
| maximal normal subgroup of | C32×C5×D7×D17, C32×D5×D7×C17, C32×D7×D85, … |
| maximal quotient of | C32×C5×C17×Dic7, C2×C32×C5×D7×C17 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 63);