Finite Group DatabasebetaFinite Group Databasebeta| order | 11936 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C4×C373 ⋊ C2 |
| Sylow | C373 ⋊ #126 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D373 |
| commutator, socle, cosocle | C22×C373 | C23 |
| Fitting | C4⋊C4×C373 | C2 |
| prime radical | C22×D373 | C22 |
| hypercenter | C4⋊C4 | D373 |
| hypocenter | C373 | #126 |
| LCS | G ▷ C22×C373 ▷ C373 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
60 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,373|b^2=de,c^2=d,b^a=bd,c^a=ce,f^a=f^372,f^c=f^3721874 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #126×D373, C2×#26045787, #37559949, … |
| maximal normal subgroup of | #126×D373, C2×#26045787, #37559949, … |
| maximal quotient of | #37559289, #37559303, #37559305, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11936, 141);