Finite Group DatabasebetaFinite Group Databasebeta| order | 11168 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×Dic349 |
| Sylow | C349 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D349 |
| commutator | C2×C349 | C22×C4 |
| Fitting, prime radical | C2×D4×C349 | C2 |
| socle, cosocle | C22×C349 | C23 |
| hypercenter | C2×D4 | D349 |
| hypocenter | C349 | C4×D4 |
| LCS | G ▷ C2×C349 ▷ C349 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
1760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36374224, D8×Dic349, SD16×Dic349, … |
| maximal normal subgroup of | #36374224, D8×Dic349, SD16×Dic349, … |
| maximal quotient of | C22⋊C4×Dic349, C4⋊C4×Dic349, #36374019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11168, 109);