Finite Group DatabasebetaFinite Group Databasebeta| order | 10878 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×#19129580 |
| Fitting, Hall | C2×C37×C49 ⋊ C3 |
| derived, Hall | C37×C49 ⋊ C2×C3 |
| Hall | C2×C49 ⋊ C37⋊C3 |
| Hall | C2×C37 ⋊ C49⋊C3 |
| Sylow | C49 ⋊ C2×C37⋊C3 |
| Sylow | C37 ⋊ C2×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #19129580 |
| commutator, cosocle, hypocenter | C37×C49 | C2×C3 |
| Frattini | C7 | C2×#11715912 |
| Fitting | C2×C37×C49 | C3 |
| socle | C2×C7×C37 | ΓL(1,𝔽8) |
| LCS | G ▷ C37×C49 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
1214 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36344154, #36344158, #36344160, … |
| maximal normal subgroup of | #36344154, #36344158, #36344160, … |
| maximal quotient of | C4×#19129580, C22×#19129580, C2×#30654553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10878, 17);