Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D349⋊C8 |
| unambiguous semidirect product | D349⋊(C2×C8) |
| derived, Sylow | C349 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #13063703 |
| commutator, hypocenter | C349 | C22×C8 |
| Frattini | C2 | C22×#13063703 |
| Fitting | C2×C4×C349 | C4 |
| socle | C22×C349 | C2×C4 |
| prime radical | C22×D349 | C4 |
| cosocle | Dic349 | C23 |
| LCS | G ▷ C349 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
728 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#13063703)⋊C8, #36375017, #36375019, … |
| maximal normal subgroup of | (C2×#13063703)⋊C8, #36375017, #36375019, … |
| maximal quotient of | C2×C4×#14584102, C4×D349⋊C8, D349⋊(C22⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 229);