Finite Group DatabasebetaFinite Group Databasebeta| order | 8384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C22⋊D131)⋊C8 |
| Fitting | C22⋊C8×C131 ⋊ C2 |
| Sylow | C131 ⋊ C8×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D131 |
| commutator | C2×C131 | C22×C8 |
| Fitting | C22⋊C8×C131 | C2 |
| socle | C22×C131 | C22×C4 |
| hypercenter | C22⋊C8 | D131 |
| hypocenter | C131 | C8×D4 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2×C4 ◁ C22⋊C8 | |
134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^6,131|a^2=e,c^2=e,e^2=f,b^a=bd,g^c=g^1301340 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D4×D131, C2×(C22⋊D131)⋊C8, #30674651, … |
| maximal normal subgroup of | C8×D4×D131, C2×(C22⋊D131)⋊C8, #30674651, … |
| maximal quotient of | #30664753, #30664758, #30664764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8384, 612);