Finite Group DatabasebetaFinite Group Databasebeta| order | 10928 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | Q8×C683 ⋊ C2 |
| Sylow | C683 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D683 |
| commutator, socle, cosocle | C2×C683 | C23 |
| Fitting | Q8×C683 | C2 |
| hypercenter | Q8 | D683 |
| hypocenter | C683 | #41 |
| LCS | G ▷ C2×C683 ▷ C683 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,683|c^2=d,b^a=bd,e^a=e^682,e^b=e^682,e^c=e^6821715 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36346037, #36346039, #36346043, … |
| maximal normal subgroup of | #36346037, #36346039, #36346043, … |
| maximal quotient of | #36345974, #36345978, Q8×Dic683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10928, 41);