Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#19129588 |
| Fitting, socle, Hall | C2×C72×C37 ⋊ C3 |
| derived, Hall | C72×C37 ⋊ C2×C3 |
| Hall | C2×C72 ⋊ C37⋊C3 |
| Hall | C2×C37 ⋊ #3861 |
| Sylow | C72 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ C2×#3861 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19129588 |
| commutator, cosocle, hypocenter | C72×C37 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C72×C37 | C3 |
| LCS | G ▷ C72×C37 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
1214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36344238, #36344240, #36344248, … |
| maximal normal subgroup of | #36344238, #36344240, #36344248, … |
| maximal quotient of | C4×#19129588, C22×#19129588, C2×#30654570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 87);