Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×D4×C337 ⋊ C2 |
| Sylow | C337 ⋊ #121 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D337 |
| commutator, socle, cosocle | C22×C337 | C23 |
| Fitting | C2×D4×C337 | C2 |
| hypercenter | C2×D4 | D337 |
| hypocenter | C337 | #121 |
| LCS | G ▷ C22×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|b^2=d,b^a=bd,c^a=ce,f^c=f^3361694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36341437, #36341442, #36341447, … |
| maximal normal subgroup of | #36341437, #36341442, #36341447, … |
| maximal quotient of | #36341162, #36341181, #36341193, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 117);