Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×#13063703 |
| Fitting | Q8×C349 ⋊ C4 |
| Sylow | C349 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#13063703 |
| commutator, socle | C2×C349 | C22×C4 |
| Fitting | Q8×C349 | C4 |
| prime radical, cosocle | C2×D349 | C23 |
| hypercenter | Q8 | #13063703 |
| hypocenter | C349 | C4×Q8 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
70 conjugacy classes of subgroups.
455 conjugacy classes — view the full character table.
| maximal subgroup of | SD16×#13063703, Q16×#13063703, #36375183, … |
| maximal normal subgroup of | SD16×#13063703, Q16×#13063703, #36375183, … |
| maximal quotient of | C4⋊C4×#13063703, #36375093, #36375095, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 227);