Finite Group DatabasebetaFinite Group Databasebeta| order | 10731 |
| isoclinism | isoclinic class of #3861 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×#3861 |
| Fitting, socle, Hall | C72×C73 ⋊ C3 |
| derived, Sylow | C72 ⋊ C3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | #3861 |
| commutator, cosocle, hypocenter | C72 | C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C72×C73 | C3 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C73 | |
40 conjugacy classes of subgroups.
1387 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D73×#3861, C73×#64424, #36339926, … |
| maximal normal subgroup of | D73×#3861, C73×#64424, #36339926, … |
| maximal quotient of | C2×C73×#3861, C73×#89204, C3×C73×#3861 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10731, 14);