Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| isoclinism | isoclinic class of D37⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C72 · Schur multiplier (H2) = C7 |
| direct product | C72×D37⋊C3 |
| unambiguous semidirect product | D37⋊(C3×C72) |
| unambiguous semidirect product | (C37⋊C3)⋊(C2×C72) |
| Fitting, socle, Hall | C72×C37 ⋊ C2×C3 |
| derived, Sylow | C37 ⋊ C2×C3×C72 |
| Hall | C72×C37⋊C3 ⋊ C2 |
| Hall | C72×D37 ⋊ C3 |
| Hall | C37⋊C3 ⋊ C2×C72 |
| Hall | D37 ⋊ C3×C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C72 | D37⋊C3 |
| commutator, cosocle, hypocenter | C37 | C2×C3×C72 |
| Frattini | C1 | G |
| Fitting, socle | C72×C37 | C2×C3 |
| LCS | G ▷ C37 | |
| UCS | C1 ◁ C72 | |
80 conjugacy classes of subgroups.
588 conjugacy classes — view the full character table.
| maximal subgroup of | C72×#3866⋊C3, C7×#15690950, C7×D7×D37⋊C3, … |
| maximal normal subgroup of | C72×#3866⋊C3, C7×#15690950, C7×D7×D37⋊C3, … |
| maximal quotient of | C72×Dic37⋊C3, C2×C72×D37⋊C3, C72×#66524⋊C2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 26);