Finite Group DatabasebetaFinite Group Databasebeta| order | 10784 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C4×C337 ⋊ C2 |
| Sylow | C337 ⋊ C22⋊Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D337 |
| commutator, socle, cosocle | C22×C337 | C23 |
| Fitting | C4⋊C4×C337 | C2 |
| prime radical | C22×D337 | C22 |
| hypercenter | C4⋊C4 | D337 |
| hypocenter | C337 | C22⋊Q8 |
| LCS | G ▷ C22×C337 ▷ C337 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,337|a^2=d,b^2=d,b^a=bd,c^a=ce,f^b=f^336,f^c=f^3361694 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22⋊Q8×D337, C2×#24924937, #36341813, … |
| maximal normal subgroup of | C22⋊Q8×D337, C2×#24924937, #36341813, … |
| maximal quotient of | #36341164, #36341176, #36341179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10784, 124);