Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C349 ⋊ C2 |
| Sylow | C349 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D349 |
| commutator, socle, cosocle | C22×C349 | C23 |
| Fitting | C4⋊C4×C349 | C2 |
| prime radical | C2×D1396 | C2 |
| hypercenter | C4⋊C4 | D349 |
| hypocenter | C349 | #123 |
| LCS | G ▷ C22×C349 ▷ C349 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,349|c^2=d,b^a=bd,c^a=ce,f^a=f^348,f^b=f^3481754 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #123×D349, C2×#26013624, #36374653, … |
| maximal normal subgroup of | #123×D349, C2×#26013624, #36374653, … |
| maximal quotient of | #36374006, #36374015, #36374022, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 131);