Finite Group DatabasebetaFinite Group Databasebeta| order | 10988 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C67⋊#4223 |
| Fitting, socle, derived, Hall | C41×C67 ⋊ C4 |
| Sylow | C67 ⋊ #4223 |
| Sylow | C41 ⋊ Dic67 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C41×C67 | C4 |
| prime radical, cosocle | C67×D41 | C2 |
| LCS | G ▷ C41×C67 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,41,67|a^2=b,c^a=c^32,d^a=d^66,c^b=c^40740 conjugacy classes — view the full character table.
| maximal subgroup of | (C67⋊C3)⋊#4223, C3×C67⋊#4223, C3⋊(C67⋊#4223) |
| maximal normal subgroup of | (C67⋊C3)⋊#4223, C3×C67⋊#4223 |
| maximal quotient of | C3×C67⋊#4223, C3⋊(C67⋊#4223) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10988, 7);