Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| isoclinism | isoclinic class of D37 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C3×C72×D37 |
| Fitting, socle, Hall | C3×C72×C37 ⋊ C2 |
| derived, Sylow | C37 ⋊ C2×C3×C72 |
| Hall | C72×C37 ⋊ C2×C3 |
| Hall | C3×C37 ⋊ C2×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C72 | D37 |
| commutator, cosocle, hypocenter | C37 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C3×C72×C37 | C2 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C3×C72 | |
80 conjugacy classes of subgroups.
2940 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C72×#3866, C3×C7×C7⋊#3866, C3×C7×D7×D37, … |
| maximal normal subgroup of | C3×C72×#3866, C3×C7×C7⋊#3866, C3×C7×D7×D37, … |
| maximal quotient of | C3×C72×Dic37, C2×C3×C72×D37, C72×C9×D37, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 100);