Finite Group DatabasebetaFinite Group Databasebeta| order | 10988 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D41×D67 |
| unambiguous semidirect product | (C67×D41)⋊C2 |
| unambiguous semidirect product | (C41×D67)⋊C2 |
| unambiguous semidirect product | D2747⋊C2 |
| Fitting, socle, derived, Hall | C41×C67 ⋊ C22 |
| Sylow | C67 ⋊ C2×D41 |
| Sylow | C41 ⋊ C2×D67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C41×C67 | C22 |
| LCS | G ▷ C41×C67 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
770 conjugacy classes — view the full character table.
| maximal subgroup of | D41×D67⋊C3, C3×D41×D67, D67×D123, … |
| maximal normal subgroup of | D41×D67⋊C3, C3×D41×D67 |
| maximal quotient of | C3×D41×D67, D67×D123, D41×D201, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10988, 8);