Finite Group DatabasebetaFinite Group Databasebeta| order | 10928 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C683 ⋊ C2 |
| Sylow | C683 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D683 |
| commutator, socle | C2×C683 | C2×C4 |
| Fitting | C8×C683 | C2 |
| prime radical | C2×D683 | C4 |
| cosocle | C4×C683 | C22 |
| hypercenter | C8 | D683 |
| hypocenter | C683 | M16 |
| LCS | G ▷ C2×C683 ▷ C683 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,683|a^2=c,c^2=d,b^a=bd,e^b=e^6822738 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×D683, C2×#24926404, #36346022, … |
| maximal normal subgroup of | M16×D683, C2×#24926404, #36346022, … |
| maximal quotient of | #36345926, (C2×D683)⋊C8, Dic683⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10928, 23);