Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | Q8×Dic337 |
| Sylow | C337 ⋊ C4×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D337 |
| commutator | C2×C337 | C22×C4 |
| Fitting | C2×Q8×C337 | C2 |
| socle, prime radical, cosocle | C22×C337 | C23 |
| hypercenter | C2×Q8 | D337 |
| hypocenter | C337 | C4×Q8 |
| LCS | G ▷ C2×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
70 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341390, SD16×Dic337, #36341397, … |
| maximal normal subgroup of | #36341390, SD16×Dic337, #36341397, … |
| maximal quotient of | C4⋊C4×Dic337, #36341191, #36341204, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 113);